Apologies if this is too basic but all the explanations about AES
focussed on the details of the protocol, not these more basic
In fact you are asking about general secret key management :)
1) Is the point of this (and other encryption techniques) to reuse the
same private key for multiple messages? If we're using one-time keys,
then a simple addition is enough and the complicated AES256 protocol
is unnecessary yes?
In theory - you can reuse the secret key for encryption directly (this is called ECB mode - Electronic Code Book mode), but then you're leaking information - see Block cipher modes. Comparing multiple cipthertexts you can see the encrypted data are the same (and having information about the plaintext it is possible to recover the plaintext and the key completely). You may want to use other cipher modes (stream, CRT, CBC, ...).
What you mean by the 'addition'? If you mean you XOR / ADD the plaintext with the secret key - you need to make sure the key in fact a 'one time pad' and really random. AES (generally any encryption protocol) is designed not to leak any information about your key or the plaintext.
And very important part - do not forget about the authenticated encryption - make sure the integrity of the ciphertext is ensured.
2) If we are using the key multiple times, how many times is it okay
to use it before the message is no longer secure? 3) How do we measure
the strength or weakness of such a protocol? I assume the objective of
an attacker is to guess the key but how is it quantified, how easily
someone can guess the key?
There is a lot of math around - depending on the key size, key usage, usage frequency and estimated adversary computing power. But keeping it practical - look for a chapter "Recommended Cryptoperiods for key types" in the NIST-800-57. It doesn't give you exact answers, but there are guidelines to be more or less secure and still usable.
4) Is it that given the encrypted and the plaintext for a given key,
how easy it is to guess the key that is used as the "standard" to
If proper encryption is used, it should be very hard. That's why you may want to use standard encryption protocols, nothing custom or simple (as you mentioned in you first question).