2. Yes and Yes
3. To 4 decimals: $0.0000. That's not being snide.
4. No
5. Yes/No/Yes. All companies know what other companies are paying for typical engineers. If you are a particular standout in a particular specialization (eg AI) then you'd have an edge by getting a competing offer, but otherwise not.
You didn't state where you are and where the job is, but I take it both are bay area.
> I wasn't really planning on leaving
Then you may be putting the cart in front of the horse. If you like your job, and like the company, are learning things, why change? I hope you realize it's completely different working for a bigco than a startup.