1. For genersl ability in the past, you can use 'could' as in,
'I could cook when I was a teenager.'
But you can't use 'could' while talking about a specific occasion when you were able to do something, for example
'I could cook a nice meal once at my brother's birthday party.' ×
'Last week, I managed to/was able to cook a nice meal at my brother's birthday party.' √
However you can use couldn't in all situations as in
'I couldn't cook when I was a teenager.'
'I couldn't cook a meal at my brother's birthday party.'
In addition we prefer 'could' with verbs like see, hear, remember, understand.
'When I was back home, I could smell something burning.'
2. You don't use could to talk about past possibilities. Instead you can use could/might/may have done or was/were able to to mean that.
3. You can use 'could' to say that somebody had the general permission to do something in the past as in
'Back in my time, we could go to school in shorts.'
4. I'm not sure how you can make a request in the past! I think it's impossible unless you've got a time machine.
'Could you lend me some money yesterday?' Well it doesn't make sense, does it?