Hey there, welcome to the forum!

To try and answer your questions from my perspective:

-Generally new to combat robotics so to anyone with experience, do you think this would work?
Your design does look good, similar type of concept to my BW, Shu! though that is a lifter, not a clamper. The clamping action will need to be quite quick I think as BW robots are usually pretty fast in the own right.

-Would a servo be powerful enough to power this? If so could anyone make recommendations
I am going to say maybe. Although a servo will work for this application, you don't want it under strain for too long otherwise you are liable to break it and the receiver I would have thought. It is heavier but I would have gone for a geared motor.

-I guess il need a lot of pushing power with a bot like this, would the standard 12v 1000rpm gearmotors be enough?
I would go with Shooty on this one and say ~500rpm motors might be a better choice for this. 1000rpm motors are OK and probably would work but when pushing, you may find it not enough against the opponent, especially if they are pushing. I'd also very much look at getting grippy rubber wheels. If you can't gain traction, you cannot push, regardless of your motors.

-What escs do people generally use for this weight class?
Shu! used a Sabretooth 2x5A in its last appearance at the European 2018 championship. I know some folk here haven't had wonderful experiences with them but its generally not been too bad for me. Azriel (my other beetle) uses a pair of fairly generic RC car brushed ESCs to move with.