Suvaratri,
Just file for TPS. TPS tend to get extended for a long period of time. That shall cover you for a long period of time. If you have the TPS and then file for Asylum case, if your case is not granted by the asylum officer your case will not go to court and that will be your last stop since you are in a valid immigration status.

Answers:

1) If your case is denied at lower court it will go to BIA then to appeal court. The process is very long and i cant give exact answer to that. May be even 10-15 years. You can take the case even to US supreme court after appeal court but they normally deny to hear immigration cases unless it is a very high profile case or it actually affects the whole judicial review process.

2) yes you can marry and drop the case. The process will go lil different though. Hard to explain everything here.

3) If you are out of status then u cant avoid it but if you have a legal status for eg TPS your case will never go to court. Its either you will be granted or denied. You wont be placed in removal proceeding.

Highly recommend you to sit down with a expert asylum lawyer. It is a very complex matter.