Comma placement with 'nor' and 'yet'

[Rayah Raouf]

Hello! I've searched high and low but cannot seem to find a clear answer to this. If you could help me out, I would appreciate it.
I've checked the comma forum, conjunction forum, and a few websites as well.

You use any of the FANBOYS with a comma if there are two independent clauses. But what about these cases.

-I don't like mushrooms, nor do I like cabbage.
-I don't sleep, nor do I eat.
-I don't think he studied for the exam, nor did he even try.

Is the comma usage here correct? It's not exactly two independent clauses. So, should I remove the comma? Plus, it's not like the use of 'yet'.
'The weather was cold, yet bright and sunny.' There is a contrast here so a comma is used. There is no contrast in the above sentences though.

[Rabiul_tanmoy250]

1. I don't like mushrooms nor I do like cabbage.
2. I don't sleep nor do I eat.
3. I don't think he studied for the exam nor did he even try.

[Kavita Shah]

Should Yet always be followed by a comma if it begins a sentence?