The first picture looks a bit like the wild strawberry plants that grow in my garden but not 100% sure.
When you have a few names check them on the database of www.thetortoisetable.org.uk, they have pics to help with IDing and will tell you if plants are tort safe or not.
It's been growing for years and I've never seen anything close to a strawberry! That'd be nice though. No berries grown down here.
I know it must be safe because Tank has been eating it for years. I just found this forum so I figured I'd give it a shot, see if anyone knows what it is.