Is there an API to retrieve bank transactions & balances?

This is what apps like quicken, ms money etc use. That is not an API to retrieve bank transactions and balances. It's a format that one can use for banking transaction (presentation layer) but not for pulling banking transactions.

How do I get my API keys to access my balance data?

The second set of API keys we need to access our balance data on the exchange is the Shrimpy Developer API Master Keys. To get your set of keys, sign up for your free Shrimpy accountand select the option to “Create Api Master Key”. When selecting the permissions for this key, ensure you have enabled the options for “User”and “Account”.

How does the balancing API work?

If there are both intercompany and intracompany lines in the same transaction, the Balancing API performs intercompany balancing across legal entities, and then intracompany balancing across balancing segment values within each legal entity. Previously, these balancing lines were not determined until posting to General Ledger.