I've noticed that on Android that files' sizes are different than the sizes of files downloaded from web browsers. Why that happens? Does it happen also on computer version of FDM?

nope, fdm didnt modify anything. its probably just the Android OS viewing/calculating the size differently than how other OS or browser do it. try copy small file from pc to android. the file probably will differ in size a bit too, at least mine did.

if you still concerned about it anyway, try download something that can be check using checksum.

Thanks for the answer.