Also, I wanted to use priority service with my application, but on Worldbridge's website it says you should not purchase it if you have any unspent criminal convictions. Would a red light violation from 2011 be considered an unspent criminal conviction?
No it's not.
The only criminal conviction you have is the DUI and that was spent in 2011. Plus you can use Worldbridge if you have unspent convictions but it just might take a bit longer to process.
Don't worry about the NHS stuff or marrying as a visitor as neither should be a problem for the visa. Just explain about trying to pay for the NHS appointment.
All in all:
- they can't refuse the visa because of convictions because the red light is not a criminal conviction and your DUI is spent.
- they can't refuse the visa because of the NHS stuff because you don't have more than £1,000 in NHS debt.
- they can't refuse the visa because you married in the UK as a visitor because you didn't actually do anything wrong. It's not illegal to marry as a visitor without a visa but you're just not really supposed to do it (if you knew you were going to marry before you came to the UK, you should have got a visa first, but if it was a last-minute decision while you were here, then that can't really be helped). At the end of the day, as long as you are legally married that's all that matters.
In short, I don't think you really have anything to worry about
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P.S. The ECO probably won't think anything of you. As long as your documents meet all the requirements, the visa will be granted. Remember that approx 98% of all spousal visa applications lodged in the US are approved.