Are there an infinity of public addresses for a wallet? If I understand correctly a private 256-bit integer determines the curvature of an EC curve corresponding to your wallet and that 256-bit integer can be consider the "private key".

Now how many "public address(es)" are there corresponding to that particular wallet?

Is there just one public address or an infinity?

I've got a related question related to change: in typical bitcoin clients, when a change public address (I take it a change address is public, right?) is given, is that change address corresponding to the same wallet that the one where the bitcoin came from?
A wallet contains a collection of keys, not just a single one.

Every private key has exactly one associated public key. Addresses are shortened forms of public keys (they're encoded hashes of the public key).

Change addresses are indeed public. Like every other address, the key for it is independent from the other keys in your wallet. Note that some clients send change back to one of the addresses the inputs were previously assigned to, in which case it's obviously the same key that is reused.