A person can volunteer in the United States with a B1 visa. The volunteer program must be an organized project by a recognized religious or nonprofit organization that provides services to the needy. A person can not volunteer in the United States without a B1 visa.
No, you cannot work for a US company from India without a visa.
No, US citizens cannot work in the UK without a visa.
Yes, US citizens can travel to certain countries without a visa.
No. You need to apply for a separate US Visa.
No. Having a visa for the US doesn't grant you the possibility to enter Mexico; you need the corresponding visa from Mexico.
Yes.
Yes. Recent agreements allow for US visa holders to enter Mexico without additional documentation -- besides the passport, that is.
As long as you have a US visa with you, you can also enter Mexico.
Yes, US citizens can travel to Germany for up to 90 days without a visa for tourism or business purposes.
Yes, US citizens can travel to Singapore for up to 90 days without a visa for tourism or business purposes.
You don't.
No, US citizens do not normally need a Schengen visa. They are normally allowed to stay for 90 days as a tourist without a visa.