Upgrading to the latest kde-frameworks/* and kde-plasma/* (5.6.4) didn't help with compositor problem too. There's also problem with clock display: too big font maybe (data to the left of time insted of under it). And also I still have old glitch with Plasma startup window in incorrect place (not in the center) but it disappeares right after start of Plasma after sddm, so not a big problem though.
New output.

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$ mv ~/.config/kwinrc ~/.config/kwinrc.bak

$ kwin_x11 --replace
OpenGL vendor string:                   NVIDIA Corporation
OpenGL renderer string:                 GeForce 7600 GS/PCIe/SSE2
OpenGL version string:                  2.1.2 NVIDIA 304.131
OpenGL shading language version string: 1.20 NVIDIA via Cg compiler
Driver:                                 NVIDIA
Driver version:                         304.131
GPU class:                              NV40/G70
OpenGL version:                         2.1.2
GLSL version:                           1.20
X server version:                       1.17.4
Linux kernel version:                   3.18.34
Requires strict binding:                no
GLSL shaders:                           limited
Texture NPOT support:                   yes
Virtual Machine:                        no
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(1, 0, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 0, 1, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(1, 1, 1, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.44882, 0.14882, 0.14882, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.50064, 0.80064, 0.50064, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.05054, 0.05054, 0.35054, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(1, 1, 1, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.3, 0, 0, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 0.4, 0, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 0, 0.5, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.3, 0.4, 0.5, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.134646, 0.044646, 0.044646, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.200256, 0.320256, 0.200256, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.02527, 0.02527, 0.17527, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.360172, 0.390172, 0.420172, 0.6)
kwin_core: ShaderManager self test failed
kwin_core: Failed to initialize compositing, compositing disabled
QXcbConnection: XCB error: 3 (BadWindow), sequence: 710, resource id: 1185, major code: 3 (GetWindowAttributes), minor code: 0
QXcbConnection: XCB error: 9 (BadDrawable), sequence: 711, resource id: 1185, major code: 14 (GetGeometry), minor code: 0                                                   
QXcbConnection: XCB error: 8 (BadMatch), sequence: 1772, resource id: 65011718, major code: 42 (SetInputFocus), minor code: 0                                               
OpenGL vendor string:                   NVIDIA Corporation                           
OpenGL renderer string:                 GeForce 7600 GS/PCIe/SSE2                     
OpenGL version string:                  2.1.2 NVIDIA 304.131                         
OpenGL shading language version string: 1.20 NVIDIA via Cg compiler                   
Driver:                                 NVIDIA                                       
Driver version:                         304.131                                       
GPU class:                              NV40/G70                                     
OpenGL version:                         2.1.2                                         
GLSL version:                           1.20                                         
X server version:                       1.17.4
Linux kernel version:                   3.18.34
Requires strict binding:                no
GLSL shaders:                           limited
Texture NPOT support:                   yes
Virtual Machine:                        no
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(1, 0, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 1, 0, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 0, 1, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(1, 1, 1, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.44882, 0.14882, 0.14882, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.50064, 0.80064, 0.50064, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.05054, 0.05054, 0.35054, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(1, 1, 1, 1)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.3, 0, 0, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 0.4, 0, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0, 0, 0.5, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.3, 0.4, 0.5, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.134646, 0.044646, 0.044646, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.200256, 0.320256, 0.200256, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.02527, 0.02527, 0.17527, 0.6)
Pixel was QVector4D(0, 0, 0, 0) expected QVector4D(0.360172, 0.390172, 0.420172, 0.6)
kwin_core: ShaderManager self test failed
kwin_core: Failed to initialize compositing, compositing disabled
QXcbConnection: XCB error: 3 (BadWindow), sequence: 1978, resource id: 1184, major code: 3 (GetWindowAttributes), minor code: 0
QXcbConnection: XCB error: 9 (BadDrawable), sequence: 1979, resource id: 1184, major code: 14 (GetGeometry), minor code: 0

And support information after "kwin_x11 --replace" with my config (no difference with compositor problem from default).

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$ qdbus org.kde.KWin /KWin supportInformation
KWin Support Information:
The following information should be used when requesting support on e.g. http://forum.kde.org.
It provides information about the currently running instance, which options are used,
what OpenGL driver and which effects are running.
Please post the information provided underneath this introductory text to a paste bin service
like http://paste.kde.org instead of pasting into support threads.

==========================

Version
=======
KWin version: 5.6.4
Qt Version: 5.5.1
Qt compile version: 5.5.1
XCB compile version: 1.11.1

Operation Mode: X11 only

Build Options
=============
KWIN_BUILD_DECORATIONS: yes
KWIN_BUILD_TABBOX: yes
KWIN_BUILD_ACTIVITIES: yes
HAVE_INPUT: yes
HAVE_DRM: yes
HAVE_GBM: yes
HAVE_X11_XCB: yes
HAVE_EPOXY_GLX: yes
HAVE_WAYLAND_EGL: yes

X11
===
Vendor: The X.Org Foundation
Vendor Release: 11704000
Protocol Version/Revision: 11/0
SHAPE: yes; Version: 0x11
RANDR: yes; Version: 0x14
DAMAGE: yes; Version: 0x11
Composite: yes; Version: 0x4
RENDER: yes; Version: 0xb
XFIXES: yes; Version: 0x50
SYNC: yes; Version: 0x31
GLX: yes; Version: 0x0

Decoration
==========
Plugin: org.kde.kwin.aurorae
Theme: __aurorae__svg__my-glowglass-lite-black
Blur: 1
onAllDesktopsAvailable: true
alphaChannelSupported: false
closeOnDoubleClickOnMenu: false
decorationButtonsLeft: 0, 2
decorationButtonsRight: 6, 3, 4, 5
borderSize: 3
gridUnit: 14
font: DejaVu Sans,12,-1,5,50,0,0,0,0,0
smallSpacing: 3
largeSpacing: 14

Options
=======
focusPolicy: 0
nextFocusPrefersMouse: false
clickRaise: true
autoRaise: false
autoRaiseInterval: 0
delayFocusInterval: 0
shadeHover: false
shadeHoverInterval: 250
separateScreenFocus: false
placement: 4
focusPolicyIsReasonable: true
borderSnapZone: 10
windowSnapZone: 10
centerSnapZone: 0
snapOnlyWhenOverlapping: false
rollOverDesktops: true
focusStealingPreventionLevel: 1
legacyFullscreenSupport: false
operationTitlebarDblClick: 5000
operationMaxButtonLeftClick: 5000
operationMaxButtonMiddleClick: 5015
operationMaxButtonRightClick: 5014
commandActiveTitlebar1: 0
commandActiveTitlebar2: 30
commandActiveTitlebar3: 2
commandInactiveTitlebar1: 4
commandInactiveTitlebar2: 30
commandInactiveTitlebar3: 2
commandWindow1: 7
commandWindow2: 8
commandWindow3: 8
commandWindowWheel: 31
commandAll1: 10
commandAll2: 3
commandAll3: 14
keyCmdAllModKey: 16777251
showGeometryTip: false
condensedTitle: false
electricBorderMaximize: true
electricBorderTiling: true
electricBorderCornerRatio: 0.25
borderlessMaximizedWindows: false
killPingTimeout: 5000
hideUtilityWindowsForInactive: true
inactiveTabsSkipTaskbar: false
autogroupSimilarWindows: false
autogroupInForeground: true
compositingMode: 1
useCompositing: true
compositingInitialized: true
hiddenPreviews: 1
unredirectFullscreen: false
glSmoothScale: 2
colorCorrected: false
xrenderSmoothScale: false
maxFpsInterval: 16666666
refreshRate: 0
vBlankTime: 6000000
glStrictBinding: false
glStrictBindingFollowsDriver: true
glCoreProfile: false
glPreferBufferSwap: 99
glPlatformInterface: 1

Screen Edges
============
desktopSwitching: false
desktopSwitchingMovingClients: false
cursorPushBackDistance: 1x1
timeThreshold: 150
reActivateThreshold: 350
actionTopLeft: 0
actionTop: 0
actionTopRight: 0
actionRight: 0
actionBottomRight: 0
actionBottom: 0
actionBottomLeft: 0
actionLeft: 0

Screens
=======
Multi-Head: yes
Head: 0
Active screen follows mouse:  no
Number of Screens: 1

Screen 0:
---------
Name: DVI-I-0
Geometry: 0,0,1280x1024
Refresh Rate: 85.0241


Compositing
===========
Compositing is not active


After applying patch from comment https://bugs.kde.org/show_bug.cgi?id=360033#c28 compositing has started to work like in good old times of KDE4. Thank you for the tip. Unfortunatelly, I'm not an OP of this topic, so I can't mark your answer with link to a bug as a solution.

google01103 wrote:relevant lines
possible bug https://bugs.kde.org/show_bug.cgi?id=360033

Thank you for your time.