The first is an interesting theoretical question. Seeing as a mission can go a week or more, does that mean they each log 24*7=168 hours of flight time? Is that all considered multi-engine time, or just the few minutes getting into orbit? Since it's technically a vertical takeoff, shouldn't they get the same "powered lift" shaft I get? Is the re-entry logged as glider time?
To the second question. No. They get their military pay and allowances. However, on an interview with an astronaut on NPR, one said they do file a no-shit travel claim for per diem while in orbit, noting "government transportation and meals provided." Thanks, DTS!