Removed the old carpet of my bedroom, the wooden floor underneath is in the state you can see in the pics

https://ibb.co/7GLXdD8
https://ibb.co/zHHgQKY
https://ibb.co/924vKpQ

End goal is to install a new carpet but thought the floor may need some work prior given how it looks

Am an absolute beginner so would appreciate any help or insights on that, especially

- the floor doesn't seem to be varnished, can I simply make it nicer by sanding it with an orbital sander? this should remove what's on the top layer?

- is there any product that I should use to clean up the floor?

- what would you recommend to fill the gaps like the one in the last pic?

Any other does or dont would be greatly appreciated too, have no idea what would work best and what I'm doing. Thank you!

A drum sander is what I recommend for this old floor. Even if you get to bare wood after sanding through the paint it will be a different color because the unpainted section has been exposed to the atmosphere.
The damaged area would best be repaired with epoxy mixed with wood flour created by a sander. Mix it with enough dust to make a thick paste and use two fillings to top off the gap so it can be sanded flush.
If you use an orbital sander you will need to start with 40 or 36 grit, them proceed up to 100 grit. Vacuum the floor after each grit.

Many thanks for the directions and advice Pete, really appreciated

Would the end result with a drum sander looks better than with an orbital sander?

Was concerned messing up the floor using a drum sander for the first time but might just rent one and be extra careful if that's a cleaner job

Yes you can damage a floor learning to sand with a drum sander. Just walk along then lower the drum slowly. Watch out for sudden stops like backing up into the cord or hitting the wall. A drum mark is not the end of the world. If you do get one, sand diagonally in an X to remove it then go with the grain, again. A hold back strap can help you to keep moving when going backwards. Going backwards will take off the most material.
The drum sander will speed up the job and insure that you get to bare wood. Paint will gum up the paper so start with coarse then work toward the fine paper just barely taking off the scratches from the earlier paper. The edger will go close to the wall using a light touch so don't work too hard. Just skim off the surface. Use a sharp scraper where the machines can't reach, using a file to keep the scraper sharp.

That's great, many thanks for this detailed explanation, that's very helpful