Ok op first STOP worrying about living with your parents, that is fine as long as they are happy and you are, kick that worry away for good.
Forget the partner issue for now it will happen when it happens, don't waste time on things out of your control.
Make a GP appointment to see if you need ADs and can get on the list for cognitive therapy.
Get your diary out and make a routine for your days, below is my recommendation.
Re job, you would probably benefit from a job around people that does not give you too much time for introspection, from your post you are spending far too much time sleeping in and waiting for your DM to return,
so set your alarm for 8.30, with the aim to get showered and fed and ready to start the day by 9.30am.
Take the dog for a brisk walk that will help your mood,
Then job hunt online, send out your CV, call anyone you know who may be able to help you,.. work solidly... until lunchtime, at least a couple of hours jobhunting, go for anything that you can do, it can be a stopgap if need be, but aim for a job as soon as possible.
Get yourself a healthy salad or soup for lunch, take 30 minutes or so then a brisk 30 min dog walk, this should keep your mood up, and your dog will be delighted!
Try and socialise with a friend or volunteer somewhere afternoons to make new friends, if there is nothing going on, continue jobhunting until say 5pm, then another brisk walk. You will then be able to look forward to seeing DM to discuss your day.
You may not enjoy a routine to begin with, but JUST DO IT (or your version of it)
Don't think about it, just stick to the routine and concentrate only on the bit you are actually doing, ie jobhunting, full focus, move on to energising walk, forget jobhunting and enjoy the exercise, focus on your dog. Enjoy lunch, then make an effort to forget food until the next meal, and focus on the next bit of your routine.
If you do this your weight will improve automatically so don't worry about that yet. Sort your mood and motivation. Fake it until you feel better.
Once you have sorted your routine in the day, plan social evening activities, do classes to meet new people, go to a gentle excercise class, yoga?, out with friends, forget those who make you feel down, they are in your past and don't matter now.
You are right time goes very fast, stop thinking, start focussing on LIVING your life, Find that diary and start now. Good luck