Terminal velocity isn’t the fastest that an object can travel. It’s just the speed at which air resistance and gravity reach an equilibrium. So it’s 100% possible to accelerate something past its terminal velocity. Whether you’re capable of hurtling a pissed off ball of teeth and claws past that threshold is more a question of your abilities than it is of physics.

IDK; what do you look like and how active are you? Terminal velocity of a squirrel is about 20mph. If you can throw a squirrel at or above that, you succeed. The squirrel being alive or dead may also have an appreciable effect on the outcome. Example, if alive it may bite or scratch you while attempting to throw it and make you fuck up.

Animal cruelty apart, you could probably increase its terminal velocity by dipping it in water first. This would increase its mass and reduce air resistance.