You don't need to prove anything anymore or to tell USCIS that you are getting a divorce...you are good to go. Only of course always keep all your information/legal papers for your records.
If you get divorce, then yes you will be eligible to apply for citizenship at the 5th year of being a resident not 3. And of course if you qualify for the rest of the requirements.
The other question is Family Law related and depend on the state you live in. Spousal support is known as alimony and normally is given when there are child involve but not restricted to. You need to check with a family law forum from your state, check with a family law attorney or just go to your state website association bar and they explain there normally what the divorce in general in your state is about.
Good luck,