1. Now that my H-1B expiration date is approaching, shall I do the notification of my EAD card to the HR and fill in the I-9 form ASAP?
-Anytime is OK.
Do they need more time to process the form?
-No, they just keep it on file for any possible inspection by any relevant US Govenment Departments.
When is the deadline for me to notify them?
-Any time.
What is the I-9 form?
-It is USCIS-Employment Eligibility Verification.
2. My H-1B status has been in the profile at the HR place for the past 6 years. What is the disadvantage if I told them about my H-1B?
-No problem at all for you tell them your h1 expiration (they actally should know it).