Short term, handpick as many as you can and squish them. I cannot say for sure if this is a true caterpillar (others here may be able to visually identify it) but I'd say it's very likely. For caterpillars, spraying or dusting with BT (Bacillus thuringiensis) is the real way to go. It is effective on many species of caterpillars, not just tomato hornworm. Most garden centers have this product. BT is just a bacteria that is harmless to humans, pets, etc -- but not so harmless to caterpillars :) It's good to have some on hand in case of hornworm, which can strip a whole plant very, very quickly.

Those are adventitious roots. They may occur in damp conditions or when a stem contacts damp earth, and in some cases when the plant has certain problems. Since you mention three days of solid rain, I assume high humidity in the greenhouse is the reason behind the roots appearing on your plant (or is it more than one plant?). They're just a bit odd-looking; they don't hurt the plant in any way. Google Images: tomato adventitious roots

My cucumbers and tomatoes seemed to be doing great - now the leaves are turning yellow/brown. My newest cucumber plant is growing tall, now the bottom leaves don't look right - it's like the leaf discolorations are more like the leaf has been peeled off, rather than bug bites or mildew This is the first year I've grown peas - pods are forming but not sure if the leaves are supposed to look they do. Can anyone offer any suggestions? I've used water/epsom salts and also fertilized. Don't know what else to do. Thanks in advance. Tomato Plant 1 and 2: Cucumbers below - first 3 pics are the newest tall one: Last but not least, my peas:

definitely looks like atmospheric ozone (pollutant) effect. Growing where there is limited air circulation as on a balcony can trap pollutants, especially overnight. A plant that could grow to 20' needs more room for it's roots than what you're providing so it is already suffering. The patio tomato varieties will probably work better for you next year.