Is this sort of short for I'm tired, we are tired, depending on context?
Exactly; if someone ask how you are (Sut dych chi?), it's rare that we will always use the full "I am tired"; "wedi blino" is fine on its own :) Wrth gwrs, you can always add "dw i" in front of it :)
no. this is terrible welsh.
rydw i wedi blino heno
dw i wedi blino heno are preferable.