caulk the cracks with a good caulk with a long life.

caulk will change color over time so paint over

caulk when done.

adjust the springs on the trim for the can light.

it should slide further into the can to eliminate the gap there.

best of luck

Most of those cracks at the wall are clearly some places where it was caulked previously and the caulk has pulled away. It those cases you should use a box cutter or a sharp utility knife to cut away the old caulk first. Otherwise, parts of it will look like crap because you will need to apply more caulk than necessary, and the old stuff will possibly keep pulling away over time.

If you haven't caulked before, here are a couple of tips. Use white latex painter's caulk with a small bead. When you caulk, do a few feet and then immediately go over it with a moistened paper towel stretched over your index finger. That will remove excess, push caulk into the crack, and smooth everything out beautifully. And latex caulk is great because you have a couple of minutes to remove it with wet toweling if you really make a mess of it, so you can start fresh. Here's a video showing how it's done; notice that the guy with the caulk gun does not try to apply a perfect bead since the wipe down takes care of any unevenness: How to caulk

As for the cracks in the ceiling, that's an entirely different problem. It looks like someone put in a drywall patch and didn't bother to use drywall tape to bridge the seams. Thse cracks are the inevitable result. Caulking that will not be a good long term solution. You need to reapply joint compound and drywall tape to those, then sand and repaint.

Use a paintable caulk in the cracks except for the ceiling. You are going to need to tape and mud the ceiling crack. If it is plaster I would use mesh tape.