You use Qt on Linux and Win32 or 64 on Windows... It is not very portable! And, if I use QT, I know another solution which works cleanly but I learnt to develop in Pascal... I like Lazarus but it is necessary to be serious...
What Blaazen said. Also, if you don't like the use of various widgetsets, have a look into the customdrawn widgetset or e.g. LCL+fpgui...
For many people, Lazarus is a perfectly usable cross platform tool. Instead of complaining in a general sense, indicating what's wrong on a more detailed level will more quicly lead to improvement.
Then Lazarus is mainly developed under Linux. Then, why all these limitations which do not exist with Windows Lazarus ? Because the ancestor it is Delphi ? With the arrival of Windows 8, it's time to put back it in question and to renew the approach of components.
No idea what you're talking about here. Lazarus is being developed on/in Windows, Linux, FreeBSD, OSX, Solaris...
One of the goals is that transition from Delphi/VCL is fairly simple.
The arrival of a new GUI - Windows 8 - does not mean everybody needs to follow that - especially in a cross platform environment. What about GTK, Qt, Cocoa? Do you want to rewrite the entire LCL when KDE4/qt would switch to KDE5?
If you don't like the LCL, why not use the FPGUI or MSEIDE products (separate from Lazarus) that also use FPC.
What is the slogan of Lazarus... I have difficulty in reading or translating... "Write once, run anywhere" 
The problem is not to know if we can develop on Linux and Windows with Lazarus. With a common code, we can obtain something solid.
As Blaazen indicated: write as much common code as possible, compile on many platforms.
There will ALWAYS be differences between platforms, regardless of the approach you take, if you go further than basic applications.
Now is it normal that I can not eliminate the Caret of TMemo under Linux?
Is it normal under Windows that I can change the color of a disabled TEdit but not the TextColor ?
Is it normal that I stack 2 StaticTexts to manage BorderSpacing on Windows and on Linux ?
If your answer is yes, to defend from such position, we can understand the so restricted number of lazarus developers.
No idea. As people said, check the bug tracker and please report new bugs so they can get fixed.
If possible with a simple example program; a patch would of course be better.
Am I too much requiring ?
You seem to be a bit aggressive but that might be a cultural thing. In essence, having similar behaviour across platforms is a design goal of Lazarus.
Then, there is another problem. The way are built some widget prevents from being able to modify them in a significant way. Things so basic as the selection multilines not contigue are not integrated into TStringgrids. Any developer does not use it? Ah, it is necessary to derived its owned stringgrid. I made it but I consider that it is not adapted to the current professional development.
Don't understand the last part, sorry.
Anyway, thanks for speaking up and trying to improve things by reporting what you think is wrong with the tool.
Because it's open source, you can influence Lazarus for the better. If you can, I would strongly suggest opening bugs for any problems that have not yet been reported, along with sample progams, indication of platform/widgetset, Lazarus version etc and hopefully an idea for a solution/code/patch.
Thanks,
BigChimp