Wow, I can completely relate. I had been suffering from moderate to severe depression on and off for the past year until a couple months ago and, after reading what you wrote, I completely understand and can relate to what you are going through.
In my case, there were times when I just had no interest whatsoever in going running. Other times I would go running and it would just be too emotional of an experience for me - for whatever reason, it would cause my emotions to really come out and I would end up crying near the end or after many of the runs that I did go on.
As for your fitness, I would say that if you don't run much, that you could (temporarily) lose some of it - I know I have - but you can also get it back. That is what I am doing right now, working on getting my fitness back from where it was. But that's for when you're emotionally feeling better, not now.
Looking in hindsight, running more than I did while I was depressed probably would have been a good idea, no matter how little interest I had or how emotional it made me get near the end and after the runs. I would recommend trying to at least keep a minimum amount of running going, but obviously no heavy training (speed work) or anything like that. Think of it as just going for a relaxing, fun run. Do it around people if you can (on a busy trail, something like that) - always good to be around people when you're feeling down!
But, with that said, there is a light at the end of the tunnel (even if you can't see it yet, it's there).
Like you've been doing, just keep taking it day by day. I know you're going through a (completely natural) really tough time right now, and I also know it will gradually get better.
And, yes, absolutely cut yourself some slack! You have gone through a lot and you are going through a lot. Just do what makes you the most happy (or as close to happy as you can get).