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It will take 5 years of living in the UK on spousal visas in order for your wife to qualify for ILR (it’s a leave to REMAIN visa so she must already have lived in the U.K. for a number of years before she can qualify).
You’re looking at 3 visa applications over the next 5 years, and I would budget around £10,000 in visa fees for them (especially if she plans to apply for citizenship too)
In order for her to qualify for a spousal visa, you need to meet 3 main requirements:
1) financial requirement (UK spouse’s UK income)
2) accommodation requirement (you must have guaranteed accommodation in the U.K.
3) relationship requirement (proof of a genuine relationship over the last 20 years)
See here:
https://www.gov.uk/uk-family-visa/partner-spouseWhether you need to go first will depend on how you can meet the financial requirement. If you can meet it without going to the U.K. first, then you can apply while you are both still in the US.
For savings, they can be in a number of accounts as long as the account are in your name(s) only and the money has been held in each account in full for at least 6 months.
Your wife will be allowed to work once she has a spousal visa.
You can receive any benefits you are entitled to as a U.K. citizen but you cannot claim extra because of your wife and she cannot claim any herself.
Caring for your elderly parents will have no effect on the application... unless you already live in the U.K., you already care for them full-time and you receive Carer’s Allowance from the U.K. government, which would mean you would be exempt from meeting the financial requirement.
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