Hey, I'm in Swansea but spent a few years living in Aberystwyth when I was younger.
To try and answer your questions:
How lonely might I be? Are there any men there? Will I make friends my age, who might be single?
Aber is a small town of about 14000 people, so you're not going to get as much choice as in somewhere like Cardiff or Swansea, but that also means you've not got as much competition. It's certainly not some tiny village with 2 eligable bachelors and thats your lot.
What kind of social life could I hope for, being single?
It's a big enough place that you'll have a choice of local pubs, be able to find things like book clubs etc. Its a university town so the population skews young, but there's certainly not a dearth of single people your age about
Is it deprived at all, or rather nice? Is it mostly safe?
Depends where you're coming from. Its a seaside town that's past its heydey, and it can seem a bit forlorn in winter when the students have all gone home and it's a bit of a ghost town, but I really liked it in spring to Autumn, and in summer its got quite a nice vibe. I certainly never felt unsafe there (although I'm male, so other peoples mileage may vary)
Does the TV show Hinterland present an accurate picture? (Aside from all the murders, hopefully).
Not seen it sorry
Does it rain a fair bit? (That's fine, just curious).
Yes, it does rain quite a bit. Aberystwyth isn't quite as bad as Swansea (which was the wettest place in the UK for a long period. Personally it doesn't bother me, I don't mind a walk in the rain.
Need to learn Welsh? (Also fine, but I might struggle).
No, not at all. The majority of people in Aberystwyth speak English as their first language. Its not until you hit north Wales that you end up with Welsh being the default language, and even then 99% can speak English fluently.
To answer your other question about other areas of Wales that might be suitable, I can recommend Swansea. It's a lot bigger that Aberystwyth, so plenty of people to meet, and while the city center is nothing to write home about (Like most town centres at the moment, theres a lot of empty shop fronts), the surrounding suburbs are mostly quite nice. And you have Gower on the doorstep, which is an area of outstanding natural beauty. Its a peninsula full of gorgeous beaches, walks through woods, windswept moors. Its a lovely place and only a 20 minute drive from most of Swansea