F-1 Visa

Yes, you can generally stay in the US while your B-2 extension or F-1 change of status application is pending, provided you file it before your current status expires. This applies to most applications filed while still in status (e.g., H-1, B-1, B-2, L-1, E-1, E-2). If your I-94 expires on April 21st and you apply for a B-2 extension or F-1 change of status before that date, you can stay in the US while your application is pending because you filed it timely.

Yes, you can volunteer while on a temporary visa as long as you are not compensated in cash or kind.
For F-1 OPT, if the volunteer work is meant to count toward your OPT compliance, it must be at least 20 hours per week and related to your field of study. If it’s purely additional volunteer work (e.g., helping at events, reviewing research papers) and not counted for OPT compliance, there’s no issue, but check with your DSO.
However, you cannot volunteer for a for-profit company, as that could violate labor laws, though the violation would be on the company’s part, not yours.
 

If you are on an F-1 visa converted from B-2, your visa stamp is only necessary if you plan to travel outside the U.S. While in the U.S., your status is governed by your I-94, which typically says "DS" (duration of status) and remains valid as long as you maintain your student status.

If traveling briefly to Canada or Mexico for under 30 days, you can use Automatic Visa Revalidation (AVR) to return without a visa stamp, provided you haven’t applied for and been refused a visa during your visit. Scheduling visa stamping in Canada is risky—if denied, you lose AVR eligibility and must return to India to reapply.