1) It is not a complex sentence; there is only one clause.
Professing his love is a participle phrase which modifies
letter.
2) a) I would use
deaths, because each person has his or her own death.
b) I would use
deaths as above, and
only children. This emphasizes that the only children they had died. (Do we know that for sure? There was a lot of unspecified dying going on.)
Sole means
one, and two (or more) children died.
One could also say
...the deaths of their own children to emphasize that they were the Montagues' and Capulets' children.