Okay so as a test I sent 2 transactions to my bitcoin wallet.
One for 0.00011792 BTC to 1Apqmd4bQBaazqvRPA4Si8LzLvGjRaf3bQ (the one I signed already)
Another for .0.00011828 BTC to 1PMHH5BHtr1WEpesJcBPBZ2FZDdfURkohG (which is address that appeared in the receive after the first transaction)
My wallet showed the sum of both addresses once confirmation was completed.
Then I sent 0.00016200 BTC back to the originating address.
The receiving block chain transaction
https://mempool.space/tx/4b941d7b2b0bc274f90d4d8310fbed3e640ffe9a5924389b73a85870b72d7cb9Shows that most of the BTC came out of the second address (emptied it completely) and 0.00001200 BTC came out of the first address, and I'm assuming carried with it a hefty fee do to the small amount in the transaction of the second address ? (Fee was like 0.00007420 BTC)
The amounts that are being transferred don't affect the total fee that the sender has to pay. The fee is determined by the number of inputs and outputs, type of addresses being used (Segwit or Legacy), and things like 2FA, multisig scripts, etc. That transaction of yours had two inputs. If one of the addresses you initially sent to had enough coins, you could have used only that input and paid less in transaction fees. A transaction of 0.00016200 BTC made up of 2 inputs is more expensive than a 1 BTC transaction that only has 1 input (if the same sat/vbyte fees were used).
So.. it seems, that the balance in my wallet, is simply the sum of all addresses in the blockchain for which I can 'sign' for with my private key.
Private keys - plural. Each address has a different private key.
a) Consolidate them amount all into one address before sending (which I'm guessing would also save me on tx fees?)
If you consolidate your inputs at a time when the transaction fees are low, you will save money when it's time to move those coins elsewhere since you will only be spending from 1 input. Remember what I said before, the amount of coins you send doesn't affect the mining fees you pay. Inputs and outputs do.
b) Send signatures for every address in the transaction to prove it was me that sent the money for all of them
(and not just 20 other random people sending small amounts)
Another reason to consolidate and avoid the hassle of multiple signed messages from multiple addresses.