The Yuan-Ti are an odd race. They come in a variety of different physiological shapes (pureblood, halfblood, abomination, and anathema), but are all (theoretically?) biologically compatible.
Serpent Kingdoms, a 3rd edition source book, says "Yuan-Ti hatch from eggs" on page 10. It then goes on to talk about breeding by logical selection of "abilities and fitness," but doesn't call out one type of Yuan-Ti versus another.
But what about purebloods, who at least look human. Is there anything like the old "Ecology of…" articles that covers it? Do they lay eggs? Birth live young? Can they mate with humans?
Best Answer
Both. They can lay eggs or give live birth.
From 5e's Volo's Guide to Monsters pg. 92
So, yes they can lay eggs, but also give live births as well. The section doesn't give the exact chance, but given with the wording it probably depends on what they mate with. The same page also answers your last question. Pureblood Yaun-tis can reproduce with humans. Though it seems only some purebloods are able to, and the rare offspring would result in another pureblood.