1. Even if you're spending a lot of time outside, as long as the gaps are less than 6 months and your primary home is the U.S., there's really no risk of losing your green card.
2. You will not consult an accountant but as a general rule, you are taxed the same whether you're living here or abroad and whether you're a permanent resident or citizen.
3. You would be entering the U.S. as a permanent resident each time.
