1) Who would Democrats run?
If he's still physically fit, probably ex-President Wilson - who after all probably still won the popular vote. If not it could b any of a host of possibles. The OTL choice, James M Cox, is as likely as anyone.
2) How certain is it that Dems would win?
Not certain , but highly probable.
1916 was so close that neither side can afford to lose any support. And, as OTL, people will be fed up with wartime regimentation and be longing for a return to normal, and the peace treaty, whatever its precise terms, is sure to leave lots of people disappointed. OTL this hit the Democrats hard, TTL it will hit the Republicans. Maybe not as hard as the Democrats were, since Hughes (who lived until 1948) probably won't collapse the way Wilson did, but I don't see him being re-elected. Pity, I like him.