I read a TL once where Murray became president. It was an ultradystopia-wank, with Murray alining the US firmly with Hitler and joining World War II at the beginning, on the side of the Nazis, using the threat of Communism as a pretext for joining.
Personally, though I think the US (and the world) are much better off without a Murray presidency, he won't turn the US into a fascist state, as was the case in that TL. That said, I think he'd use questionable tactics if it suited him politically and he won't be above trying to exploit fear in society to win a second term
Assuming he lasts until World War II (which as stated earlier, is questionable), I see a strict nutrality stance as the most likely outcome, as far as US-German relations go.
My knolidge of Murray is almost non-existent, but I got the impression he was a New-Dealer. I imagine he'd try and implement something relatively simelar to the New Deal in office, for the sake of keeping himself popular if for no other reason... I have a hard time seeing him get as much done as Roosevelt though.
I think it's more likely than not that Murray will lose renomination in 1936 and that Long could be a contender. I'm not sure who else they could run-their's Richie of course, Smith and Garner will also probably run-but I don't think either will be nominated. I don't have all that much knolidge of 1930's internal Democratic politics however, so I could well be wrong. Having said that, if FDR isn't the nominee in 1932 for whatever reason, a successful convention challenge over president Murray in 1936 is very likely, in which case the New deal is tried 4 years later. The Democrat will probably win the 1936 election in any case unless things get radically worse, as Hoover and the Republicans are still a vivid memory.