The subject ground cover was planted 3 weeks ago. It was just discovered that there are holes in some of the leaves. Is something attempting to eat these leaves? I use to have Hostas planted in the same spot and had the same type of holes, which I assumed were made by slugs. Please advise what you think and if it is happening by some insect, and what do I do to control this problem?
Yes, it sounds like Slugs.
Here is an article that will help you.
Is this a perennial I live in zone 3 will it survive here
Ajuga is a perennial Hardy in zones 3-9. This article may help
What can I use to kill bugle weed?
This article will help you.
the plant is doing very well in the shade, but read that it'll be okay in sun too. I like to propagate it and move it around the garden to cover as much ground as possible. Seen that I could propagate it also by root clippings that are placed in a shallow container or seeding tray and lightly covered with soil. Couldn't I just put those roots in the ground instead?
Rooted cuttings are, by far, the best method of propagation! There is no real need to germinate from seed if you already have an established plant that divides, readily.
Theoretically, you could still plant seed, though some would likely not make it. You have the best thing at your disposal, though. Divide when possible.
This article will offer more care tips: