yes, if you can convince the PD that you are a safe pair of hands
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.
ENTRY to the US would be doubtful with a criminal record, especially if the crimes are felonies.
Get a working visa, and use it. Apply for and get permanent residency.
There is a guide to conversion (US to UK) at the related link and may be helpful.
Yes, the only requirement for applying for a GB licence is UK residency, citizenship is irrelevant.
If they have a business (B-1) visa, permanent residency, or a business sponsored visa (i.e. H-1B).
There are literally hundreds of pediatric residency programs in the US.
You would have to obtain a license to practice within the US. I believe this would involve testing or passing of a designated exam, and then a residency.
This isn't an issue for US citizens. However, for foreign nationals holding legal permanent residency in the US, the US considers you to have abandoned your US residency if you spend more than 6 months out of the country.
Assuming youre a UK citizen, you are no longer eligible for the Visa Waiver Program and would require a visa to visit the US. Moreover, the deportation record would make it difficult for you to get said visa, or even get residency in the US based on a marriage to a US citizen. If youre happy with never visiting the US, you should be fine.
You do not need to be married any particular length of time to apply for US residency. Once you are married to a US citizen you can apply for residency right away. The process takes about 6 months to complete.
A General Surgical Residency is on an average of about 5 years.