Is the Bitcoin Transaction ID also the "Hash of things to sign" for the signature generation? As a random example, is the transaction id:

114be7fea4d3dd0cf2e88a8fa9a56d4ea741efbabd07d61d08cf0810be2254fd

Also the hash that was used as the "hash of things to sign" for the "signature generation" for this transaction?
No. The transaction id contains the signatures. But you are making the signatures at the same time, so it can't possibly be the hash that is being signed. How to redeem a basic Tx? describes the actual sighashing algorithm.