Hello and welcome to COL, and don't worry about your post being long
To answer some of your points (I'll give them the same numbers that you have):
1. It's possible that he was spoiled by his previous owners and given treats, food off their plates, scraps when they were preparing food etc. and that has made him food obsessed. Having said that, it's a bit of a Cocker trait anyway, although your boy sounds a bit extreme. I think I'd persevere in ignoring the whining etc. (easier said than done, I know) and hope that he eventually realises it's getting him nowhere. Is he up to date with his worming and does he look a good size and shape, not skinny? What do you feed him? Some foods just don't seem to satisfy some dogs, so it would be worth considering a different food to see if that helped.
2. Don't give him any more opportunities to chase sheep, ever. I know you didn't anticipate it happening that first time, but TBH you're lucky he wasn't either shot by a farmer or that you haven't had the police round. Not sure if you realise this, but farmers are entitled to shoot dogs that are chasing or threatening their livestock. Your dog could have attacked, even killed the sheep he chased, and at the least will have caused it a great deal of stress and if it was in lamb it may have aborted the lamb. They don't grow out of it, so please make sure he never has the opportunity to do it again. He might not be as lucky next time. Lecture over, but please, please take note of it
Personally I wouldn't encourage dogs to chase birds either. I'm sure he has fun, but while he's doing it he's out of control and it's probably increasing his chase and hunt drive.
4. Sounds like you're doing well with the separation anxiety. He's only been with you for a short while and is still adjusting, so I'm sure he has times when he feels a bit anxious. If it's improving then hopefully he will continue to do so. Dogs are social animals and generally don't like being alone for too long. Cockers are usually very people oriented and can suffer from separation problems more than some other breeds.
5. The usual rule of thumb for puppy walks is 5 minutes per month of age, so around 50 minutes or so at a time is fine. That can be done more than once a day and the amount of exercise you're giving him sounds OK to me. I'm a horse owner and know that with horses you want them to be fit for what you're doing with them, but not too fit. For instance a child's pony doesn't need to be as fit as a racehorse! So you do steady work to get the horse to the level of fitness that you want and then try to maintain it there. I believe it's much the same for dogs. Unless you're working a dog I think it needs to be fit enough to do the amount of walking that suits it's age and lifestyle, but if you keep on increasing exercise it will keep on needing that amount or may become bored and frustrated. Mental stimulation in the form of training and games can be just as tiring and can leave the dog feeling in need of a sleep or period of relaxation.