basically homomorphic encryption is being able to perform mathematical operations against encrypted values. So you can for example add two numbers and get an accurate result (also encrypted) with zero knowledge of the underlying values before or after the operation.

The ENCRYPTO group put together an implementation of garbled circuits protocols called Tasty a good while ago if it helps anyone. https://github.com/encryptogroup/tasty

Sure, I've just published more details taken from the documentation:

https://www.calctopia.com/2017/02/01/on-the-security-model

Absolutely not: outsourcing the secure computation to third-party servers is not on the first release.

The secure multi-party computation runs between the computers of both participants (over LAN/WAN).