So I started thinking: Am I correct, that when sending a bitcoin transaction, all of the amount from a specific address gets placed in the input, a part of it (the part which I specify) gets sent to the address I wish to send, and the rest gets transferred to a newly created address on the same wallet, from which the send operation was initiated?
Not "all" of the amount. It uses a UTXO (Unspent Transaction Output) as input and send you back the change for it.
Basically, a UTXO is the output of a previous transaction you received. The way your wallet handle this is also called "coin control".