Sounds to me as if there was just some dirt or rust inside the volume pot.
Get yourself a good electronics cleaner spray/contact spray (sooner or later you'll need it anyway!)
Spray it into the pot (there should be an opening in the pot casing) and move the pot a couple of dozen times from fully open to fully closed.
That should clean the contacts within the pot.

If it doesn't help: re-solder the wire connections to the pot. One at a time, so that you don't get confused with the cables, in case you don't have a wiring diagram and you're not really familiar with that stuff. Soldering by itself is pretty easy to do.

Yes, you can do that with every guitar.
Take off the knobs. If they have a screw on the side, you need to loosen the screw first, because it fixes the knob on the pole (see pic)



If there's no screw, you simply pull it off vertically (some are sitting pretty tight, others might come off easy). If you can't pull it off with your fingers, use a flat screwdriver. Cover the guitar body with carton or cloth so not to scratch it. Use the srewdriver as a lever, lifting the outer edge of the knob slightly. Turn the knob by 90° and lift again, turn again, lift again.......the knob should come off easily then. DO NOT USE FORCE!! Just slightly lift carefully each time.

Under the knob you'll find a nut with a shim underneath fixing the pot to the body. Remove the nut (counter clockwise) and the shim. Now you can push the pot's shaft through the body wood and can remove it from the electronics cavity in the back.

Clean the pots and the switch as described.

Installation is vice versa. Make sure not to mix up the pots! Otherwise you'll have to do it again because volume is tone and tone is volume then (positionwise) ha ha ha.
At the end you simply push the knob onto the shaft. If there's a screw, tighten it carefully to fix the knob on the shaft again ..... DONE! :)

If they are mounted to the body wood, YES! You just have to remove the nut first, then you can pull it out with your fingers to the back side of the guitar.

If they are mounted to a pickguard, you need to remove the pickguard to get to the pots. :)

In your case, the pot shafts go through the front body wood of the guitar. So do as discribed in my other post.

Post pictures with the knobs removed, please.