I'll answer these, but a quick caveat: though a historian by training, it's been years since I studied WWII in any sort of depth. So take all this with that grain of salt.
First, the obvious: he tried to conduct a war on two fronts and one of those fronts was Russia. A war on two fronts is suicidal.
Agreed, but bear in mind Pearl Harbor forced his hand. Prior to that, the war on the Western Front was just about done. France was subdued, the Brits were hunkered down on their island, and it was going to be a while before anything happened there.
Then the Japanese attack the US, and Germany has little choice. Hitler was livid about the attack, incidentally.
All of which is moot, because it was doomed from the start. They - the Germans - were never going to be in a position to beat the Russians on their home turf, and after what happened with the division of Poland, Stalin would not have trusted any attempt at a truce/cease fire. A German defeat was essentially inevitable.
It's a matter of numbers, like if we took on China. Yeah, we're more modern, have far better projection capability, and all that... but they outnumber us so badly that the moment we hit their home turf all they'd have to do is keep coming at us.
Never get into a land war in Asia. Remember that.
Second. The Battle of Dunkirk. [...] If he had pressed his advantage and wiped out those forces, and followed that up by an immediate invasion of the U.K, things could have turned out differently Could he have held the U.K. once he got it?
Lemme look this one up again, but in lieu of that, I seem to recall Hitler never planned to invade the UK immediately. The goal was to bomb them into submission, get them to agree to some sort of cease fire, recognizing that, much like the situation the US faced when we were staring down the potential invasion of Japan, that it was going to be very, very ugly if it came to troops on the ground.
Eventually would there have been an attempt to conquer the UK? Of course, but in the short run Hitler was content to simply have them stop fighting the Germans. Bear in mind, the Germans were working on rockets, and this was meant to be the ultimate way to eventually - key word there - bring the UK to heel.
It was recognized that unlike France, conquering the UK outright would more than likely bring about US involvement all on its own. It was one thing to let non-English speaking nations fall; quite another to bring down the parent country of the US (and it's northern neighbor and still UK territory*).
*Least I think Canada was still, at that time, not yet fully independent. I expect the Canadians here to correct me if I am wrong.