Regarding the black marks on the leaves, I suspect they are a physical injury, and not something you'll have to worry about in the long term. In your shoes I would keep an eye on them, but nothing more for the present. I don't know what to make of the odd new growth, and can't see enough detail in the picture of the opening bud to have an opinion about it.

Could be a fungus like Vladimir said, could also be an insect egg or just dirt on a bit of fluff. However, I'm more concerned with how dusty the leaves are. I may just be dust or it could be the beginnings of a spider mite infestation. It's a good idea to wash off the leaves from time to time, like maybe every 4-6 weeks. Take them outside and hose them off, or if that's not possible, put them in the shower and shower them off with cool water. Then let them drain well and put them back where they were. It helps prevent spider mites as they're attracted to dusty plants. And your plants love the rinsing off!

I think my tomato plant cannot be saved. I did some more research and I think the plant has the Tomato spotted wilt virus. Early symptoms in a young plant include inward cupping of leaves and leaves develop a bronze cast followed by brown spots. Once the plant becomes infected the disease cannot be controlled. My plant has all of the above symptoms. I purchased the plant at a big box store and it has always been outdoors. My picture does not show bronze leaves because I cut them off.

It's not powdery mildew, but I checked closely under some leaves and I think it is spider mites. I'm going to try Neem oil, but any other suggestions for something not too toxic would be appreciated.