Each club will have a different ethos; mine's more about road riding with very few racing and a new MTB section. They're social through to more serious.
1. It shouldn't matter what type of bike, although the type of club will almost dictate that. It goes from the HSBC-sponsored
Let's Ride through to racing clubs with the latest kit such as
Rapha CC. My club's got riders on all sorts of bikes, hybrids through to the latest carbon - and in most cases there's no snobbery.
One thing to think about, seeing you're female, is whether they have a ladies section or even be a female-only club. Mine began a ladies section about 4 years ago when riders from several clubs wanted to form their own sub-group and have their own rides / kit / events to help women ride more. It's been a brilliant idea, with a greater range of rides and more partners joining as well.
2. Age-wise you'll probably have to be over 16, otherwise it's a junior club and there's lots of those.
3. If it's a British Cycling registered club there'll be a committee. The club secretary is usually the point of contact.
4. British Cycling's Clubfinder will help you find one:
https://www.britishcycling.org.uk/clubfinder
5. Diabetes should be fine, although I'd let them know when you join. That's a minor condition compared to some.
6. Most members are fine; those that aren't tend to find themselves out on their own. I've had a couple of bad experiences when considering joining a club; one local one didn't want new members and another said I was too fast for them
. I've had a couple of riders be an issue in mine - I have my own way of dealing with them, usually up steep hills
7. No test, but most clubs will invite potential members on one of their shorter or beginner rides just to check. On a couple of occasions my club's had riders who couldn't ride more than a couple of miles slowly try to join their long weekend ride that's at speed. We've got beginner's rides for that purpose and a more social sister club.
My suggestion is to find a few clubs local to you, look at their website / social media pages and select one/two that are of interest. Make contact. I found mine because they rode on Saturday's and bumped into their riders a couple of times - they seemed (mostly) sensible.
You're likely to be covered under their insurance for up to 5 rides. After that you'd need to join and pay a membership fee plus insurance, usually through being a British Cycling or Cycling UK member.
Where are you based? There's probably CC members nearby who know of the different clubs, and may even be a member.