Plenty of people commute around the country. Mainly those new commanders who relocated for a promotion or new FOs still waiting for their choice of base.
There are, however, a number of pilots (CPT + FO) on the 737 fleet, full time, that commute from various European countries and don't seem to have any issues doing so.
And yes, days off are paired nicely. I'm not sure if that's a rostering agreement or the way things work out on my roster. But I generally get 2-4 days off in a row in the summer. You can also bid to have your work in blocks.