Find a job that will sponsor your H1B visa, fly over, find a place to live. Stay for a few years and apply for residency and eventually citizenship if you really like it. Larger corporations generally have the resources to support paperwork more easily.

I don't know the specifics. That's just what the staff at Aldi said when I asked. Aldi Corporate probably didn't think spending the money for a liquor license was worth it or would force them to raise prices.

No, because of NH's liquor laws. I moved here from Georgia and was disappointed like you.