Are they in the right places?

don't know about the others, but
Persian Shield needs shade, & celosia full sun;

I water my celosia about twice a week for about a minute,
& it's doing well.

If you disturbed the roots of celosia when you planted them, they may struggle. They HATE it. It is one of the plants I grow from seed for that reason.

Not sure about the others.

If they are wilting for no particular reason you probably have a soil fungus. It's really common and watering won't help. This fall, when you are removing your dead plants, put corn meal in your beds and mix it in. Yes, the cheap kind from the grocery store. I wouldn't bother planting any plants in that bed this fall. Add more corn meal in the spring before you plant. Over time, that will help combat the fungus. Hope this helps.

Carla in Leander

The persian shield gets shade all day long save for maybe a couple hours.

The celosia get full sun most of the day save for late in the evening.

When you say you water for about a minute, are you watering with a garden hose?

I didn't plant the plants, a landscaper did. I might just have him pull them up and plant something different, as these things aren't doing that great at all.

Anyone else have any ideas?

Some plants just need alot of babying depending on where you are. I've never had good luck with celosia, so rather than try to grow it, I just plant other things. I've not tried Persian Shield although it's gorgeous, it just seems like it might be one of those plants that needs more attention than I'm willing to give. It does need consistently moist soil.
Instead of celosia, try something like the profusion zinnias, or the star series zinnias (haven't seen them in the nurseries this year tho).
Insead of persian shield try something like mona lavender (plecanthrus)or the tradescantias with purple leaves.
Your liriope will probably be ok after it establishes. It's a pretty tuff plant.
Gardening is pretty much trial and error. I usually try something a couple of times, and if it doesn't work out, I move on....

Another thing to think about, they were planted just a few weeks ago...the heat is tough on transplants and maybe they need some time to recover. With all that being said, persian shield starts out green and goes purple (at least in my experience) and I just yanked all my celosia because the heat was cooking it and it looked awful.

yes, I water with a hose;

plants that can't get along here without a sprinkler system just have to return to the great universe (compost).

I actually think plants do much better without a sprinkler system. Without a sprinkler system you aren't forced to think about timing the watering. Timing's for cooking, not for watering. Check the soil, look at the plants and "read" what they're telling you, check the soil again, and then, if it's dry, water until the ground is good and soaked.

This has been such a strange weather year that it's no wonder plants are looking bad. It's not all that uncommon for liriope to have brown tips, especially if it's planted in the sun. It might also not like your water, but there's nothing you can do about that. Cut the liriope back next winter, around late Jan. to late Feb., and the new growth should look a lot better. Cutting it back now won't do any good, though. Celosia likes it hot and dry and sunny, but it's been humid and wet for most of the summer. Maybe you could whack your Persian Shield back some. It'll probably start looking better once the weather cools down a bit.

Good luck.

Sally