1. I understand the use of hashing in PoW, but what's the point of using SHA-256 to generate bitcoin addresses? Security doesn't look too important here, as we obtain these addresses from public keys, not the private ones.

2. What are the advantages (or disadvantages) of the newest generation of SHA3 Keccak hashing function vs SHA2-256?

3. Is the only benefit of hashing transactions their compact representation?

It's just to get shorter addresses. Regular public keys are 65 bytes long, which is much too long to be convenient. Compressed public keys are 33 bytes and could potentially be used instead of hashes, though these are a little longer than 20-byte hashes. It also seems likely that Satoshi didn't know about compressed public keys or wasn't comfortable with using them when he designed Bitcoin.

Hashes seem to help against certain attacks (some attacks against ECDSA, for example), though they also open up the possibility of other attacks (such as attacks against RIPEMD-160). It's not clear to me that they do improve security overall.