(background- I was a US green card holder for 13 years and naturalized last November.)
1. The same chances as anyone else, really, as long as you meet the criteria.
2. In short, no, because you have to meet a physical presence requirement in the US to be eligible for naturalization (as well as still maintaining the US as your permanent home.) There is a provision for maintaining your permanent residency for naturalization purposes while living abroad, but that usually only applies in the case of a job transfer of a permanent resident by an American company, or for military personnel.
Green cards can be valid for up to two years after leaving the country (one year without a re-entry permit, two years with a permit.)