I will try to keep this short and stick to answering just the questions you asked...
The 2nd question is easy- you will still get paid, you are still a Naval Officer and still have a job outside of flying. If on flying orders, or even not on flying orders but have met flight hours "gates", you will still get flight pay.
I assume the first part of your question is whether you will get to keep flying- it depends. You cannot fly ejection seat aircraft if pregnant. You cannot fly single-piloted aircraft while pregnant (this means solo, there are also some caveats that apply if you were instructing students that would restrict you from flying). You cannot do shipboard flying if pregnant. In general, you would stay attached to your squadron, but you cannot deploy if pregnant and current Navy policy does not require you to deploy until 12 months after the baby is born. (Though you can fly within those 12 months- I can't find the information right now on how long after the baby is born until you can fly. Standard maternity leave is 6 weeks.) If your squadron deploys while you are pregnant, it will be a case-by-case basis what you would do during that time.
If you are not single-piloted or in an ejection seat, if YOU desire, with your OB's and Flight surgeon's approval, you request through your commanding officer to continue flying and can do that until the start of the 3rd trimester. Still not deployable.
If you are a flight student, your training will stop and you will basically be on medical hold until after the baby is born. In that case you would likely be "stashed"- given a temporary job at the squadron, wing, or base where you are.
Your reference for the above information is the OPNAV 3710.7U, see chapter 8.
All OB care is covered by Tricare.
That covers flying, medical, and getting paid. There are a whole lot of other issues associated with you not being able to fly that I won't touch in this post unless you want to ask those questions.
I am a P-3 pilot, almost 24 weeks pregnant with my first child (baby girl!). I am participating in a Navy test program called the Career Intermission Program where I am taking 19 months off active duty to have a baby. One of the many reasons (and NOT the most important) for doing this is to lessen the impact having a baby will have on my career.
Happy to answer any further questions.