Is my account balance publicly visible? If I'm sending someone my wallet address, am I making my account balance visible to him?

As far as I understand, all transactions are public, which means that if I know an address, I can reconstruct the current account balance via the blockchain.
If your business partner knows your address, they can learn the transaction history and balance of that address. Often it is possible to guess or deduce that other addresses also belong to you, but this requires a bit more effort and is less reliable. However, this certainly doesn't translate to your complete wallet's balance and activity to be known.

This is why Bitcoin users are advised to generate a new address for every business interaction they have and why generally Bitcoin software makes it easy to create new addresses.