Two plants I would like to know the name and how to kill them. Thanks!

1. first photo, background, tall, thin, single stem, fluffy plant. Can tolerate it.
2. first photo, in the middle and detail in the second photo. They look like wild blackberry. Thorn. But never see them flower and have berries. Hate this one.

Looks like dog fennel and blackberry, also present is pokeweed.

The reason that you don't see the blackberry bloom and produce fruit... it does that on second year canes... I suspect that you remove them before they get a chance to bloom.

I usually just hit that stuff with a string trimmer and call it good.
When I'm trying to grow something else... I shovel-dig the blackberry briars. They have roots that run along just under the soil for several feet, so they usually return.