"Hefin is the groom"
Translation:Hefin yw'r priodfab
Yes you could use "yw" instead of ydy. The reason "Mae" isn't used here is because it is an emphatic sentence. This basically means that the most important thing comes first for emphasis. So "I am Ellis" becomes "Ellis dw i." because my name is the important part and the verb follows.
No, you can't have 'mae' and 'ydy' in the same sentence since they are effectively the same verb.
Your suggestion would translate as:- The groom is is Hefin.
The only way to express this in Welsh is the above, although you can reverse the order to have the same effective meaning.
Hefin yw/ydy'r priodfab = Y priodfab yw/ydy Hefin