So I recently bought a used bike from a person and I wanted to remove the front derailleur without taking off the chain, since I don't have a chain tool. I also do not have any equipment that could cut through the cage of the front derailleur.
If the rear most part of the derailleur is riveted the answer would be no. If the rearmost part is held together with a screw, then removing the screw and the derailleur mount clamp (typically a 5mm allen or a nine mm hex head bolt) will allow removal. You can purchase a chain tool for about $15 and a masterlink for about $5. This purchase will allow you to perform chain maintenance and replacement for many years to the future.
Often yes. Many front derailleurs have a small screw-bolt holding the cage closed.
If your front mech cage is rivetted or formed of one piece of metal, then you're stuck and will have to cut the chain or the front mech.
Your other option is to simply do nothing - the front mech is not a significant source of drag as long as it is well-adjusted. Simply use the limit screws to lock it in one place, using it as a chain guide.