Yes US citizens need a visa.
Yes, you do need a visa.
Yes if you do not have any valid US Visa. No if you have a valid US Visa.
Yes, it is possible to get a immigration Visa to stay in the country if you came in on a tourist visa. You will need to contact the INS and apply. Each case if different.
Right. Even on connecting flights, you need a visa when entering US soil.
Yes, a Ukranian national would need a visa to enter the US.
You need a Us Visa
If you are from a country that requires a Visa, then yes a child of any age will need a Visa.
Yes, unless you are already a US citizen you will need an immigrant visa that permits you to work, not a tourist visa.
No. Having a visa for the US doesn't grant you the possibility to enter Mexico; you need the corresponding visa from Mexico.
No. You need to apply for a separate US Visa.
Currently, Belgium is under the list of countries that are eligible for Visa Waiver program in the US. So a Belgian citizen need not apply for a visa to enter the US.