Is "tawelwch" also OK instead of "Byddwch yn dawel"?
tawelwch!/tawela! from tawelu can be used. (Tawelwch is also a noun meaning 'quiet, a silence, etc'.) There is also tewch/tawch!, taw! from tewi.
Can this be mynd allan?
That's what I put and was marked wrong
No, that is not a command form. It just means 'going out'.
The command forms are explained in the course notes.
I thought "Tawelwch neu cer allan" worked but apparently not.
No, because that is mixing a chi--form with a ti-form.
Tawelwch neu cerwch allan is fine, for example, as both commands are chi-forms.
What's wrong with "Bydda'n dawel neu cer allan"?
The 'ti' form of the imperative of 'bod' is 'bydd', so the correct 'ti' form of the sentence would be 'Bydd yn dawel neu cer allan!'
Said many times in my classroom !