Perennial candytuft aka Iberis sempervirens can become woody and should be cut back after blooming. After 3 or 4 years it tends to die out in the middle and often will need to be dug up and divided. With landscaping fabric, that might be difficult to do, but not impossible. It grows from a central crown, so it does not root along the stems.
For slugs I find shallow containters cheap or stale beer works great. Diatomaceous earth sprinkled on the ground also works well. Use the food grade and do not breathe in the dust.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.