You can use a visa if you have one or you can enter under the Visa Waiver Program and stay for up to 90 days- since France is a participating country under the VWP.
A visa is automatically given, for 90 days, when you debark in France with your passport. It will be stamped in your passport. Yes. They need a US passport to enter France and a visa to travel within the country.
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 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.
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Yes
Yes
No need for a visa, as the UK is a participant in the Visa Waiver Program.
Yes, US citizens need a visa to travel to France for stays longer than 90 days. For short visits of up to 90 days, a visa is not required for US citizens traveling to France for tourism or business purposes.
No. Having a visa for the US doesn't grant you the possibility to enter Mexico; you need the corresponding visa from Mexico.