Yes, to enter US visa is a must. Depending on the purpose of your visit the category differs from A to Z. For example B-1 is work visa, B-2 is tourist visa, F-1 is student visa etc.
You need a Visa to enter the US because that is the laws of the US. This helps reduce people trying to enter the US illegally.
You don't need a visa to enter Mexico if you are an American, Canadian or European citizen. If you, however, are from other country, even when entering from either territory you need to have a visa issued by the Mexican government.
Yes, a Ukranian national would need a visa to enter the US.
Yes.
Yes
Yes
yes
No need for a visa, as the UK is a participant in the Visa Waiver Program.
No. Having a visa for the US doesn't grant you the possibility to enter Mexico; you need the corresponding visa from Mexico.
I do not think an Indian with a US visa needs a visa to enter Puerto Rico
Yes, US citizens need a Visa to enter and exit Costa Rica.
Most definitely
Yes you do