"Is the bag free?"
Translation:Ĉu la sako estas senpaga?
I'd say it's correct.
It sounds unusual to me because I'm not used to such heavy verbing in my Esperanto but it should be fine.
senpaga "vrs" libera....Why not use either word as they both mean free?
Because they don't mean free in the same sense.
"senpaga" means "without charge".
"libera" means "enjoying personal rights or liberty".
If someone offers you free beer, they are not meaning that the beer is not in captivity, so you can't say "libera biero". And when someone says "the slaves are free" it does not mean that you can have a slave of your own without paying, so "la sklavoj estas senpagaj" is also wrong.