How can I run a script before sleep (sleep button) and after waking a laptop? Something like pm-utils use (/etc/pm/sleep.d/my-script.sh). Is Solid responsible for those tasks? I tried searching but couldn't find something relative.

try the pm-actions manual

This should be included as an option from KDE as it uses it's own (?) mechanism to suspend.

I suppose by now that there isn't a way for this, so I will fill a feature request. For Solid?

Currently, Powerdevil is responsible for handling Sleep/Hibernate actions, so the request should be aimed there I suspect.
However it is quite plausible the interface for interacting with the sleep/hibernate system will be moved into a more shared location in the future.

I filled a bug report (for Solid) couple weeks ago.

https://bugs.kde.org/show_bug.cgi?id=313693

Should I change something?

That feature request looks fine as far as I can tell, and is assigned to the appropriate maintainer. You will now need to wait to see if they implement the feature. If they do, it will appear in the next feature release of KDE, which will be KDE 4.11 at this time.