Is it possible to make watches at home without many tools, or alternatively is it possible to buy the parts you want for a watch and build it at home? I don’t mean a digital watch but an analogue watch using gears etc.
Sure, in theory, why wouldn’t it be? All you need is the knowhow and tools. Coming by those, however, might be tricky.
Is your real question whether you can purchase a kit or something? I did a brief search online and found nothing. Yes, I found watch kits, but basically you design the face and the band, and the timepiece is already supplied.
But it’s possible. I once built a wall clock from cardboard. It came from a kit, and all I had to supply was glue, varnish, pins, and pennies. Didn’t work though. 
Probably not if your goal is a functional watch. Making mechanical watches is extremely fussy work, and it takes quite a bit of expertise. You’re trying to get very precise measurements out of very tiny parts. Some guy following an instruction sheet is unlikely to build anything useful, I imagine.
You’ve never taken the back off a watch and looked inside? You should do it and ask yourself the same question again.
Buy a cheap watch and see how long it takes you to do nothing more than take it apart piece by piece without destroying the pieces. Now put it back together. My Dad did watchmaking as a hobby, which really meant that he fixed watches, he didn’t make them from scratch and many times he needed to consult with Mr. Jenkins, a retired professional watchmaker he knew. Man, I loved going with him to Mr. Jenkins house. His garage was a metalworking wonderland for a 10 year old kid.