Although it should suffice, healthy plant growth is more likely with 2-2 1/2''. (Did you remember to use some aquarium soil fertilizer? )
It depends on what plant it is. Is it just stems or is it a plant with roots? For the first, I suggest to weigh them down with a little rock. Don't use the lead wrapper it came with. That should take care of it. If it is a plant with roots, then dig it in deeper, but not beyond the rhizome. Also, put a few rocks around it. Don't plant it in the filter current and keep digging fish out until it has grown new roots (a few weeks).
It is small discs of that moss, you poke the rooted end through the disc then bury it acting as a sand anchor, personally I like using small pots set into the gravel with an appropriate soil in them, that way the fish don't uproot them so often.