I don't like Firefox because of it's predominant position. I see it as a kind of Microsoft Internet Explorer in a different costum...

So I use as well as I can other. Especially I try already years ago to use Konqueror (the old embedded Konqueror in the old Puppy Linux 1.0 .. 1.5 with it 50 Mb ISO was so a kind an effective littel browser able to manage all important jobs at this time, about 10 years ago...) but I must have the realism to constate that Konqueror did not already return to the same point it did have in the past ...

It would be sometime better to directly use a browser from the Geko family because of the integration of the provided plugins and extension in you distribution!

Are really in KDE integrated Geko browser available?

I don't know of any browsers built on KDE or QT technologies which use the Geko rendering engine. QT does provide a WebKit rendering engine which is used by a few browsers including Konqueror (select View -> View Mode to switch between the built-in KHTML and WebKit engines), Rekonq, Arora and Qupzilla. Of these it looks like only Konqueror and Qupzilla support any kind of extensions/plugins (and neither one provided an easy way to search for and/or install new extensions).
Opera is also built on Qt, iirc they recently switched from their own custom Presto engine to WebKit. Opera has its own set of add-ons which is pretty extensive.
Alternatively, you could always go with something non-KDE/Qt, like google-chrome/chromium (considering your stance on corporate ownership I would suggest chromium which is the fully open source browser that google-chrome is built on, very extensive collection of add-ons which should cover everything you used in firefox), Maxthon (not open source? provides both desktop and mobile browsers for the major OSs), or epiphany (Gnome's built-in browser, now called simply "Web").

What extensions do you use? Perhaps your needs could be fulfilled by other means?