Some Bosmer have beards. I don't think I've ever seen a Altmer with a beard, though.
I think there was enough of a culture gap between the Dwemer and other elven groups that interbreeding would have happened only rarely. The Dwemer split with the Altmer early, didn't they? After all, they were already settled in Morrowind before the coming of Veloth and the Chimer. And the Chimer didn't get along with them very well - they were warring off and on until the time of the First Council, so I don't think they would have mixed all that much. I can't think of any reason it wouldn't have been possible, though.
Well biologically, all men and mer can reproduce and create fertile offspring. Really Argonians are the only Tamreilic race (and maybe Imga) that can't produce fertile offspring with men and mer.
But, though there might have been a cultural divide, I don't think half-breed children were impossible. First off, there were always the Orcs, allies to the Dwemer at many point. A Dwemer-Orc was probebly something )however uncommon) that existed. And then there's always [censored]. Dwemer have very low moral standards. If one were to [censored] a Chimer woman, then the Chimer would probably scorn the child but the Dwemer might very well adopt the child. Then, for all intents and purposes, a child raised Dwemer IS Dwemer.