Can a particle that has non$-$zero rest mass $($equal to m$0)$ ever reach the speed of light?

Yes. You just need to give it an amount of energy equal to m$0$c$2.$

Yes, but it will require a much larger amount of energy than m$0$c$2.$

No$,$ because a massive particle traveling at the speed of light would have energy $1/2$ m$0$c$2$which is more than its rest mass energy.

No$,$ because a massive particle traveling at the speed of light would have infinite energy and would therefore require an infinite amount of energy to accelerate.