Is it obligatory for a VPN service provider with servers in the United States to disclose a user's personal information (such as IP address and logs) in response to a request that came from another country? For example, for a legal investigation or similar reason.
The title and the contents of your question are totally different. The title is "will they disclose my information", which is likely the most relevant thing for you. The contents is "are they obliged to disclose my information".
What actually will happen: The company will ask itself three questions: 1. Will we be in trouble if we provide this information? 2. Will we be in trouble if we don't provide this information? 3. Do we want to protect the customer in this situation? In a case where I was slightly involved, question (1) was answered with "no, no trouble for us", question (3) was answered with "absolutely not, we don't protect people making prank calls to emergency services", and therefore question (2) was never looked at.
So if your US ISP receives a letter say from German police that certain logging information is likely to help them solve a murder case, that ISP will ask themselves the same questions.
No. A VPN provider will be liable under the laws of the country it is in. Because countries are sovereign other countries can't enforce their laws.
What can happen is that other countries can put pressure on your country to require cooperation between you and your country and your country and them - depending in the laws and relationships between the countries. Powerful countries like the USA can very powerfully convince other countries to help them. (Its not identical, but related - in NZ there is an ongoing saga of "Kim sitcom" where the USA has effectively got NZ agencies to act extra judicially to enforce their will (over copyright issues). But it was the NZ agencies that broke down his door and killed his dog....