2. I expect fraction of Putin supporters among Russian immigrants to be highest among people immigrated in 1990s - many (but definitely not all) from this generation continued to watch Russian TV while living abroad. In 1990x Russia had relatively free press but Putin slowly turned it into a propaganda tool and this slow transition allowed Russian TV to keep old audience.
3. Support of Democrat/Republican IMO has little to do with the support of Putin or Russian government. I don't even think Republicans hate Russia less than Democrats. Trump showed a fondness for Putin but didn't do anything that would benefit Russia, quite the opposite. If you are not in a partisan bubble choice between Democrats and Republicans is not the choice between good and evil, it is an attempt to choose a less evil one. Russian immigrants know too well that socialism failed in the Soviet Union and Democrats talking about socialism can be enough to tilt the scales.