Welcome, Kim
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In regards to your questions:
1. You can marry on the normal ESTA visa. A fiance visa is only needed if you intend to live with him permanently in the US after the wedding. It even says on the US Embassy website that if you will continue to live outside the US after the wedding you should marry on the ESTA:
https://uk.usembassy.gov/visas/fiancee-2/2. You'll need to be married first, as you must meet all the requirements for the visa on the day you submit the online visa application... and one of the requirements is that you are married
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3. He cannot switch from a visitor visa to any other kind of visa from inside the UK, so he will need to be in the US to apply.
4. The best, easiest and cheapest option is to marry in the US and then apply for a spousal visa from the US for him to move to the UK.
5. Not having past passports is not an issue. If he has previously held any passports, he just needs to give as much info about them as he can, and explain that they have been lost/stolen. A minor criminal record is not usually an issue... If it only resulted in a fine, then as long as it happened more than 12 months ago, it will not affect the visa. It should be declared on the application form, and he'll need to include any paperwork he has from it (like court records/police records), but it shouldn't affect the visa decision.