Possibly alyssum. Please wait for a second opinion or research photos for your own cross reference since I'm not positive.
If it is alyssum it's ok to feed. But not in huge amounts because it can affect calcium absorbtion. My tort likes it.
It looks like two different types of plant to me. The top could be a type of sedum, the bottom looks like purslane. A non blurry image of the top one would help for that one, the bottom one is a best guess.
I don’t know what it is but it’s not alyssum. And it’s not purslane. I don’t think phlox either.
@Jesus'torts, can you get us a less blurry photo, as Will has suggested. I also think it may be a sedum but I’m not good with that plant. There are some spots on there, are they blue flowers, maybe? White flowers? That helps.
Here are some sedums, there are many kinds so it wouldn’t necessarily look identical.
It appears that the plant in the top photo could be one of the types of creeping phlox. It is frequently used as a groundcover which fits with its location under the tree and on what seems to be a hillside.