secondly there are no random numbers being generated when creating a signature (both during message signing or transaction signing). everything is being done deterministically, meaning nonce is generated using your key and the message utilizing HMAC function.
Wrong, k value must be randomly generated. 2 signature with same k value can be used to find out private key of your Bitcoin.
k has to be a number that can not be guessed. that is why it is suggested to choose a random one, but later on they realized that you can't rely on RNGs so they came up with a new idea to generate it deterministically using your private key and the message being signed. that is why when you sign same message with same private key you always get the same exact signature. check out RFC-6979 for more details.
in fact nowadays most wallet only use an RNG once per wallet and that is when you create the wallet to generate your seed then every future private key and every signature's k is being generated deterministically without needing RNGs anymore.
I'm stand corrected, i completely forget about RFC-6979 and thinking about ECDSA in theory.
