Well, I thought that you had a bed of wild strawberry with groundsel and wild radish in it, but when I looked at the next two pictures I realize I'm wrong. I don't know what they are...sorry. If the plant in that last picture has yellow flowers that turn into red berries, then yes, it is wild strawberry. And its edible, but I'm not sure about my I.D.
If you indeed have the wild/trailing strawberry plant then yes, it is fine and they will also munch the fruit itself when in season....as long as that is not all they eat then even the fruit is fine while it is in season....
I have one CDT that wants nothing to do with the strawberries in his yard but will munch the flower and a leaf once in a while....
cool....just make sure that the farmer does not use insecticides nor herbicides.... and all as part of a balanced diet...(kinda sounded like a commercial huh...LOL)
I don't think it is dandelion....however when I first looked at the pic you provided Sow Thistle came to mind.....google and look at all the images for Sow Thistle and see what you think? The only thing that made me not say Sow Thistle is that here (california) the leaves are so different than what you are showing in your pic????
the other one does look like an ornamental strawberry. I wouldn't get strawberry leaves from commercial growers if I were you, though: production of the crop is very chemical intensive.