looks like a katydid ;-) ... some sort of locust ?? ... not sure what the correct name is but we used to be fascinated with them as kids, finding their skeletons attached to trees every summer ...

Pic isn't clear for me to see what I'm looking for so here is a guess... Do your stems have lots of black dots on them that turn into long black lines,eventually turning the stem black? If so I have some kind of sucking insect that seems to spread a virus that starts out as a bunch of black dots on the stem,turn the whole stem black-not sun purple. Sometimes it ,most times it effects only the branches the bug got to. I've had all but a couple branches get messed up and eventually die. If it's what I had,it doesn't seem to effect the branches without the bug bites.But the bug bites are not just 1 or 2 per plant/branch. The bug bites are a bunch at a time,close together. If it is a fungus,try Sulfur. Whenever I use Copper it seems to do more harm than good. There are several fungusides out there with 10-14% sulfur. Just NEVER use it with an oil or during the day.Spray it EARLY morning or sunset. If you use it withing a month of using NEEM or similar oils you can kill your plants(been there,done that). Oil reacts with sulfur to make a plant poison/Toxin under different conditions. I think some bug leaves a toxin that causes what I'm talking about since when it starts out it mostly effects the branches that were bitten. I've seen a plant bie except for a couple branches that didn't get the bites marks. Here is a link that might be useful: oil and sulfur

I've read about ants making nests in the roots of a tomato plant, with the result being a dead plant. I think the problem is that they remove enough soil that the roots dry out. Here are some home remedies which shouldn't affect the tomatoes: = Sprinkle diatomaceous earth (DE) in a ring around the nest. When ants walk through this, it pierces their exoskeletons and they will die. [DE is a rough white powder, the fossilized skeletons of diatoms, a type of algae. It is sold in some garden centers. You could also try agricultural supply places or stores that feature organic foods and other natural products.] = Mix 1 cake of yeast with 1/3 cup of sugar and 1/3 cup of molasses. Put it in low lids near the ant nest. Ants love sweets and will take it back to the nest; the yeast will expand inside their bodies and kill them. [Freeze whatever you don't use.] = Crush grains of white rice with a mortar and pestle. Sprinkle it around the anthill. The ants will take it inside the nest. It will expand inside their bodies and kill them. (Some people use grits instead of rice. Powdered tapioca should work too.) = Mix 1 part sugar with 2 parts borax. Add enough water to make a gel. Put this bait on squares of cardboard or low plastic or metal lids (low enough that ants can enter and leave easily; you can also raise the dirt around the sides of the lid to make a ramp). The ants will take this back to the nest and they will all die. [Too much borax isn't good for tomatoes, so don't use a lot of this in the garden.]

IME, sooty mold does not flake off easily. It needs to be washed off. It is harmless on its own but if a heavy covering - like above - it can prevent the plant from photosynthesizing properly. Often products used to treat the insect problem causing the development of the mold - insecticidal soaps, horticultural oils - will help to loosen the mold as well, but spraying with a solution of soapy water (regular dishsoap is fine) and then hosing down with just plain water will be most effective.