lol …
1. Your CN is very low, it should be current in October which is the official start of your FY. Unfortunately, your visitor’s status would have expired before you become eligible to file for AOS as a matter of fact (and not just before you complete the process). The earliest you can file for AOS is October (or August/September if taking advantage of early filing which I typically don’t recommend for folks who are current in Oct., first month of the FY). So if you’re eligible to apply for TPS before your current status expires, you can go ahead and file for TPS ASAP, since you can AOS from an approved TPS compared to asylum pending. In order to be successful with filing for AOS with TPS status, you will need to withdraw your pending asylum application though just so you know.
2. You can apply for AOS while the TPS application is pending, the AOS application however will not be approved until after the TPS application has been approved. I have no idea how long it takes for TPS applications to get approved, that is something you’ll need to research on your own though in order to decide if the switch will be worth it. In the other hand, it is not too late to withdraw the asylum application, depart from the US before your current status expires and process CP from your home base if able to safely do so.
3. Correct.