Can't help you with some of them, but...
Up north the second is known as "silver dollar". If you hate where they're growing, yank them out and save some of the dollars (the seeds are in them) and then plant the seeds in an buried pot. See if you like them and go from there.
Your berry plants are just holly -- one plain, one variegated. They out-grow the cute stage, and they will grow outside of designated location.
The English ivy, the one you hate, grows out of control and is perhaps better rooted and used in planters as a ground cover, low growing planting. They hang very nicely and are a pleasant addition for planters.
As far as the succulent grassy things, I've seen them before but don't remember their names. I don't remember them being particularly intrusive--they sort of keep to themselves and will sprout a lily-like stem of flower.
Good luck with your garden...
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