if I only worked in the US from the age of 15 to 23, am I eligible to claim any benefit from SS when I get to the appropriate age?
As per DurhamLad's post, you need 10 years worth of contributions under the US system. The UK pension requires a minimum of 10 years of qualifying years of National Insurance. If you don't have 10 years under either of the UK or US systems, but do have 10 or more years combined, you should be able to combine them for eligibility purposes (but not per-scheme payout purposes). i.e. you would get separate, small, pensions from both. If this is you, Google "UK US Totalization Agreement" (or wade through
https://www.ssa.gov/pubs/EN-05-10199.pdf, page 7 onwards).
Note that if you end up with both UK pension and US Social Security payouts, your US Social Security payout will likely be reduced by something called the
Windfall Elimination Provision that you'll need a spreadsheet to work out (but never exceeds 50%)
If you've had no UK qualifying employment (i.e. never worked in the UK), the story isn't over yet :-).
You should first check you aren't entitled to 'free' years under the UK system from non-employment activates (such as certain types of child care and unemployment schemes, etc). These activities are listed at
https://www.gov.uk/national-insurance-credits/eligibility. It's not a complete list though as I think it only lists the ways credits can be obtained today. We're more interested in credits you accumulated historically (whether you were in the country or not). In particular, if you turned 16 between 1975 and 2007 I would expect you to qualify for 3 years of historic credits due to a policy designed to level the playing field between those leaving school at 16 and those staying on (This was a blanket policy based solely on your birth date. Nationality, location, and whether you were in school or not didn't matter).
If you still don't have 10 combined years, two ways to get additional years under the UK system are:
1. Get a job that pays at least £120/week, or
2. Make voluntary contributions for the missing years. This will probably cost around ~£880 per year.
https://www.gov.uk/voluntary-national-insurance-contributions/who-can-pay-voluntary-contributions is a good place to start.
And what would that age be?
If you are disabled, I think you can start claiming at any age. Otherwise the earliest you can claim is 62, but it's at a reduced rate. If you were born after 1960, full rate starts at 67, otherwise enter when you were born into
https://www.ssa.gov/benefits/retirement/planner/ageincrease.html to get the full retirement age specific to you. Same page will also show you what the reduction would be if you pick an age between 62 and full retirement age to start claiming.