It looks like your basic 'Concord' type Vitis labrusca grape, probably one of the earlier cultivars like 'Worden'.

Bayer Admire Pro. systemic

There is no typical skeletonizing in your images. The common Grape Leaf Skeletonizer is not associated with webbing, so your caterpillars may be Leaf Tiers or Leaf Rollers, too small yet to deform the leaves. In any of the above, Bt would be effective. The adult moth that layed the eggs may well be done for the season, so picking off the leaves might be the end of it.

I recently identified the tiny grapes I've been enjoying as "champagne" grapes, otherwise known as the black corinthian or Zante Currant variety of grapes. If anyone has a vine, I would like to trade for some cuttings. If you have an large grape variety that is sweet and good table fare, I also might be interested. I have cuttings of "Anastasia" Kiwi berries of both male and female(though the females are pretty good at self fruiting alone) as well as Flame Seedless grape. I also have a semi large collection of heirloom vegetable seeds (~100 variants) and some specialty plant seeds such as the Szechuan buzz button, groundcherry, and mouse melon so feel free to ask and I'll send you a list to see if anything catches your interest. Have a good day!