Self-pardoning is a crazy scenario that up until this presidency would seem to be just a crazy hypothetical. Even Nixon dismissed the idea when presented with it. I like Vox's round-ups of legal opinions on these sorts of topics, and in this one there's a much greater diversity of opinion about whether a self-pardon is doable.
https://www.vox.com/policy-and-polit...on-impeachment
The general take-aways: there's nothing stopping him from doing it, but there's also nothing stopping federal prosecutors from proceeding anyway and arguing before a judge that his self-pardon is invalid; how those courts would decide is anyone's guess. But it can't shield him from impeachment (and criminal proceedings could only more forward after he's no longer president). It also can't shield him from state prosecution, and there are a number of state crimes (including money laundering and fraud) that could be turned up by Mueller's investigation that fit within state law. And based on the context, there's real possibility that the threat of self-pardoning could be considered obstruction itself.