Looks like Primrose Willow (Ludwigia) sp. Not in the Willow (Salicaceae) family.

Looks like a just a regular old clump of blue phlox, which bloom this time of year. The are not a shrub, just a medium size perennial flower that can spread slowly over the years. See this picture as an example: http://www.pocketpoems.info/resources/blue%20phlox2.jpg

Sqare stems are an indication of the mint family. What kind of mint, I'm not sure. Sorry I can't be of more help. I've heard of something called watermint..maybe that's it? April

For your tomato, it looks like Flea Beetles, you can actually see one in the bottom-most picture you posted and the damage is typical of them. Treatment for Flea Beetles depends on your personal preference. For the non-organic route, I believe you can use Sevin insecticide - provided they are listed on the bottle, which I believe they are. Organic pesticides, on the other hand, I don't know of any for killing Flea Beetles - I'll defer to those with experience on the matter. I don't use any pesticides really, but if I had them, I'd just squish as many as I could find :) For your Basil, it kind of looks like it's got sunburn / windburn. Was it hardened off before putting it in full sun? For the cucumber... I'm guessing it's probably not warm enough yet for it to really take-off growing. It looks fine and pretty much like most of my seedlings. They always start-off slow and then try to conquer the garden in a matter of weeks. Good luck.