ENTRY to the US would be doubtful with a criminal record, especially if the crimes are felonies.
No, marrying a U.S. citizen does not automatically convey permanent residency or citizenship. The proper procedures for obtaining resident status will need to be followed by the non-citizen, the issue of a criminal record may play a significant part in a decision by the USICS. (www.usics.gov)
Once you are officially married to an American citizen, you can not be deported from the country, unless you engage in a criminal offense.
No.
No, that is not a basis for permanent residency. You are only allowed to stay the amount of time allowed in your visa (usually 6 months) or if you entered under the VWP then you can stay for 90 days
Whether a US citizen can work in Japan is completely unrelated to that person's UK residency status. It is a matter for Japanese law and regulations.
No.
You dont. sorry
He is a citizen. I do not know why you think he is a criminal, since he has not been arrested and is the legally elected president of the United States. You may not agree with him, but that does not make him a criminal.
Yes. If their mother or father became a US. citizen then legally if they're under 18 they are a citizen.
Her residency will not even be asked about, nor allowed to be brought into evidence, as concerns custody, even if she were illegal. You prepare based on the whole of the case, not on this issue.
It's not illegal.
Only if you apply to become a Canadian citizen. Once you get residency in Canada you can apply for provincial healthcare.