Yes, it is possible - no objections from the Romanian part; the problem is in the USA.
Practically citizens from all the world can travel in Romania; for details ask the Romanian embassy in your country or see the link below.
Yes, a non-Romanian may divorce a Romanian in Romania without being present in court there, even if the marriage took place in Romania. This is possible only if the non-Romanian has the permament domicile outside Romania. The way to do this is for the non-Romanian to give a Power of Attorney to a Romanian lawyer for representation in the Romanian divorce court (Art. 614 of the Romanian Civil Procedure Code). Gabriel Triculescu www.proimmigration.com
You can get a passport to anywhere no matter if you are married to someone of that nationality or not. If you want to go to Romania that go with or without a romanian husband or not. You can become a Romanian citizen if you marry a Romanian and therefore get a Romanian passport.
it is complicated. you must live for 5 years i think in Romania and the take a test from romanian history and literature. it could be quicker if you get married with a romanian citizen.
This depends of your country of origin; see the link: http://www.mae.ro/node/26966..
You don't need Romanian citizen papers for marriage.
After 3 years of legally married with a Romanian citizen, you can apply for a parmanent residence (Romanian Passport).
No it does not make him a citizen, but it you may sponser him for citizenship if you wish.
No! Bigamy is forbidden by the Treaty of Brussels, to which both Romania and US have signed.
A person can get a fiancee visa by filling out a form called the K1 fiancee visa. Requirements are that both are eligible to get married, have met in person the last two years and the person is a U.S Citizen.
Yes, it is possible but only with Romanian visa and an invitation from a relative in Romania, approved by the Romanian Ministery of Internal Affairs. See the table in the link, including the note for Egypt: http://www.mae.ro/poze_editare/2009.06.10_Anexa1_ro.pdf
No you will not become a Mexican citizen but you will have Mexican recidency. Your fiancee can have the option to apply for citizenship later on if she wants.