Bonjour. En anglais parce que mon francais n'est pas tres bon

Edit: tre=>tres. Whoopsie. And yes, I don't do accents, too lazy, sorry.
Thanks for trying out Lazarus and glad you like the support

Summary: post your Windows and Ubuntu Lazarus/FPC versions. I think you may have an older version on Ubuntu which shows some bugs.
Long version:
Re first subtlety: modifying the registry to show calendar? I thought ludob showed you a way to do that without having to modify the registry?
Regardless, I think it's a good idea to respect the user's regional settings. If he configure his OS that way, it's his decision which week is which week number, I'd say.
(Exception: multi-country international software for a single organisation. In this case it makes sense to temporarily override the OS selection)
Second subtlety: don't know about that one. May be because your Lazarus version on Linux is too old.... and lacks support for properties that are on your windows version.
Third subtlety: might be because your Linux Lazarus version is too old (i.e. bugs have been fixed since). As you say, it may be a widgetset limitation, don't know. You could try with qt instead of gtk or vice versa.
In these cases, it is good to ask on the forum as you did, if this is a known problem. You could also look through the bugtracker to see if this is a known, open bug. Or perhaps this was an issue that has been fixed in a certain Lazarus release (in which case the bug on the bugtracker should be closed).
Finally, there is also a custom-drawn widgetset that does not use Qt or Gtk. Have a search through the wiki for details; e.g.
http://wiki.lazarus.freepascal.org/Roadmap. Haven't used it myself and it looks as if you will need a recent Lazarus version for that.
There have been multiple discussion on why existing widgetsets are used. I think it often boils down to the balance of "native look and feel for all applications - Lazarus and others - on a platform" versus "same functionality on all platforms for a given Lazarus application". Often, theres is emphasis on the former choice.
Yes, you could use LCL-FPGUI, which is sort of a bridge to use the fpGUI components using LCL (the Lazarus equivalent to the VCL). I myself would look into the customdrawn widgetset first, because lcl-fpgui is dependent on yet another layer, while customdrawn draws things directly, which would make it less error-prone.
By the way, when you post, could you include Lazarus and FPC version as well as operating system, as well as other relevant details - i.e. in this case the widgetset you use? See
http://wiki.lazarus.freepascal.org/Lazarus_Faq#What_is_the_correct_way_to_ask_questions_in_the_forum.3FThis will help people respond with more precise answers.