Adobe Reader shows "Validity unknown" on e-Aadhaar because it does not have the Indian root certificate. This page checks the signature itself on your device and tells you if the file is genuine.
Adobe does not trust India's root certificate by default. It does not mean your Aadhaar is fake.
The first 4 letters of your name in capital letters followed by your year of birth, for example RAHU1990. This tool does not need the password.
No. The check runs in your browser.