Tips & advice for a few fixes

Hi all,

I recently moved into a new to me home, and there's a few little bits and pieces I would like to go about tidying up - for now I was wondering if anyone might be able to give me a few pointers on fixing a few cracks & gaps.
A building inspection was done a few months back, and these issues were pointed out, and deemed to be cosmetic. There's a few walls that need a patch up paint wise, and I'd like to tidy these parts up at the same time - and I'm interested to learn how to do so properly.

There's a crack above one of the door frames, a crack extending from a ceiling corner. When the windows have been replaced, there have been gaps left between the trim and plasterboard.
Just wondering how those with experience would recommend going about tidying these small issues? Before I use the wrong tape/filler/caulk etc in the wrong places

Thanks!