I'd not expect reinstalling the packages- at least on a unix-style OS- to have any useful effect.
First: can you confirm that you're using Lazarus, not the text-mode editor etc.?
Assuming that you're using Lazarus, I think that the two things you need to be looking for are a directory named ~/.lazarus or similar (I'll spell that out since I don't know your unix/Linux experience: a directory named .lazarus in your home directory, the leading . will prevent it from showing up in ordinary file listings) which contains the Lazarus configuration info including a list of recently-used files etc., and a file named something.lps in the directory containing your project which contains the specific state of that project i.e. what files are currently open etc.
I'd expect an ordinary Lazarus Compile, Build or Run (all in the top-level Run menu) to all save your project files (something.lpi, something.lpr, something.pas etc.) and then to compile. It's usual for a new user to start off with a very simple program with nothing but a standard button on a form... make sure you've got that and don't try anything fancy until you've got some level of confidence in what's going on.
I don't know how many Mint/Cinnamon users there are around here, I use Debian/KDE. I suggest- strongly- that if these problems persist you tell us /what/ version of Lazarus you've got, what processor it's targeting (even if x86, there's 32- and 64-bit variants) and where you got it: was it packaged by Mint or did you get if from the Lazarus site? Each time you start a separate problem I suggest putting that in the first msg, DO NOT put it in your sig since every time you edit that it will affect every message that you've ever posted so there will be no ongoing archive of what compiler/IDE version was causing you which problem.
MarkMLl
p.s. sorry if I'm rather curt: I'm currently trying to focus on a geometry problem and having a hard time.