Trumpet vine gets flowers? Haven't noticed flowers on either and summers almost over.The first looks like a trumpet vine. Not dangerously toxic.
The second may be one of Euphorbia sp. formerly called Chamaesyce. If so, it will bleed milky sap when cut. Alternately, that could also be one of the morning glory clan.
Yikes! Says do not feed in tortoise table because it contains oxalic acid but he has been consistently eating it and seems to really like it; very strange.The second picture is "prostrate knotweed" aka polygonum aviculare
It's not toxic at least. While large amounts for prolonged periods could be an issue. I would pull up as much as you can from his enclosure especially before it goes to seed. Once it gets going it can choke out other plants. I consider it to be more of a nuisance than a threat.Yikes! Says do not feed in tortoise table because it contains oxalic acid but he has been consistently eating it and seems to really like it; very strange.