Depends on your citizenhsip. If you are granted a visa waiver program then you need a visa only if you intend on staying more than the specified time allowed for you. If not, you need a visa and yes, you can be able to process it while in the US, given that your visa is not yet expired.
How long can you stay in the USA on a esta visa
It depends how long does your visa allow you to stay in the US.
O1 visa
no they dont
You dont need a visa. Its part of the Visa Waiver program between US and UK
St Maarten/St Martin is part of the Netherlands Antilles, not a US territory. So, yes you will need a passport and obtain a visa while you stay there.
Citizens can legally stay forever.
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.
No, 6 months is the maximum visa free stay. After that, you need a visa.
A Polish national is REQUIRED to have a visa to enter the U.S. So, without a visa, a Polish citizen cant enter the US at all- period (never mind how long he can stay).
Medical insurance is not required to obtain a US visa however if a visa is granted some programs require that you have medical insurance during your entire stay in the US
Once can stay as long as their visa or immigration papers allows them to