Are you supposed to use add mesh (ctrl a in edit mode) or use multiple objects to make more complex shapes?
Depends on what you're going for but yes generally the rule of thumb is if you're doing something more complex, Shift + A in edit mode is how you do it. Object Mode you can consider for whole, complete models so you can move them all around a scene as different pieces. Edit mode is properly modifying them to look like whatever you desire them to look like. If its supposed to be one whole piece then you would do it there (like a character, though I've also seen some people separate hair and clothes into objects and bind them to the same armature if they want those to be swapped out. But if you don't, like making clothing pieces or furniture or just a simple object in general, then it wouldn't be much of a concern).
If you do Shift + A in Edit mode, it becomes part of the object. If you do Shift + A in Object mode, it becomes another object. There are also more intricacies, like median points, but I don't think you want to hear all that just yet.
If you use multiple, is there any way to texture paint without dealing with merging everything into one object?
I'm not entirely sure what you mean when you say this? Do you mean having them all connected to the same texture without having them to all be the same object? Because if it is then just give both objects the same Material by going to the Materials tab, clicking on the little ball with the down arrow next to it underneath the blank list thing, and then it should show all of the materials in the project, including the ones of other objects, where you can go from there.
Is sculpting better or proportion move or dealing with extruding stuff?
It depends on what you're trying to do. No one is really
better as it really depends on what method you're doing when you're going into it to begin with.
That all being said though, unless you already have experience in sculpting from the get-go, I'd say start with hard-edge/vertex-type modelling (the one with planes, cubes, and cutting or "extruding stuff" as you put it, I don't know the
exact professional term for it lol).
When do you apply subdivisions?
Generally whenever you're done enough that you don't think you'll need to make changes because Subdividing is going to add too many polygons and things for you to edit as easily later (you can, but it's just a bit more of a pain).
Just as a suggestion, it might help if you see someone more experienced use the program to model things actively. That's how I learned back in the day. Unfortunately, the person I used to watch stopped doing that a long time ago but they do still have some things (not the same I used to watch but still) up on
their YouTube channel that might be helpful. They don't do any sort of guiding through the process, it's more to see how someone does use the program to it's full potential. Maybe there are other 3D modellers on there you can watch as well on Twitch too if the speed-modelling goes by too fast. I promise not all of them are doing these crazy like, high end builds that you could never do in a million years (though it might be a little tricky to find them since the simpler things don't get as many views).