A field guide for moths would help for identifying these little winged creatures, but I don't have one yet. I'm pretty sure the last moth pictured above is a staghorn cholla moth. The staghorn cholla is a common cactus around here. I can't recall ever seeing a moth on a cactus, probably because most moths are nocturnal.
Last year I saw a tiny emerald moth and a sulphur butterfly on a cottonwood leaf by the creek:
And two years ago, I saw this colorful moth on the wall, possibly a Nevada tiger moth:
That's about it, have a great week!