Are there any exceptions to allow a kohen to marry a divorcee? And after the wedding does take place, is it a valid wedding? Are the children of that marriage mamzerim? Are they considered kohanim? Is the groom still a kohen and can he duchan?

A Cohen can't marry a divorcee. No exceptions. If they do get married the marriage is valid and they most get divorced. The children of this marriage are Kosher Jews but Chalalim i.e. not Cohanim. The groom is still a Cohen but can't deprived from Cohen privileges and shouldn't "Duchan" or get first Aliya in shule. (See Shulchan Aruch EH 6; ibid OC 128, 40)