Garden Pests

i'd love for someone to help me out with some of my garden mysteries (and how to solve them).

mystery #1: unknown plant (or weed) this reminds me of some sort of beetle eating the leaves, although i have never seen any foliage eating insects in my life. if you look closely, there is a small speck of an insect in the middle of the plant (which may or may not be the culprit). this plant is located in the front flower and perennial gardens of my house, and the other plants and myrtle around it appear to be unaffected.

mystery #2: peony

i purchased 2 small white peony plants and dug a hole in the ground and plunked them in. i have no idea how rich or ordinary the soil is. but as soon as i planted them, the leaves turned dark red, and this one's leaves started to curl. there is no other signs of rotting or disease so far as i can tell. they seemed to have survived the transplant though, and now the leaves are turning back to green. sadly, they were very young and i planted them late. so i don't think they will flower this year.

mystery #3: hydrangea

my hydrangea is starting to bloom! again, a purchase of a smaller perennial (they are cheaper and take transplant better) transplanted into a hole dug in the ground with no working or enrichment of the soil. apparently i have alkaline soil per the pink blooms, but the tips of the leaves are starting to darken. i wonder if the hydrangea and the peonies are suffering from the same problem as they are planted in the same plot.

ideas?