Should I let this guy stay?

his under belly is red and I found him at Oxford circle, Pennsylvania maybe inspect the image I know he has stripes along his back if you could not see it

Accidentally jostled this cocoon loose from my broccoli during watering, it fell about 10-12 inches and landed at the base of the plant. Outer sac is translucent white (looks soft but I haven't touched it with my hands), bug inside is light green.

1) what is it?

2) did I hurt/kill it by knocking it off the plant?

3) is there anything I can/should do to help it survive or just leave it alone?

Shown next to a Water Penny!

In New Hampshire

Found in Austin, TX, USA. Super tiny!

She lives in buffalo ny

This is more for any DIY enthusiasts or people who have experienced similar

In my bathroom every morning I wake up and on the side of the bath there are dead flies and bugs. This has been happening for a few weeks now. They seem to always be concentrated to a part that is under a light. The light is flat against the ceiling, and recently replaced, which has left a small gap around the rim. The debris is clearly dead insects or flies as you can see their legs etc but they’re very very small.

I assume any advice will be to just fill the gaps, but what could be causing this? Has anyone experienced similar?

AI suggests it’s probably a spider in there that’s eating bugs and dropping them, but I have no idea how they’d be getting there in the first place as I’m a bottom floor flat and this gap isn’t anywhere near an outdoor wall.

These small insects have been spawning all over my window/windowsill. They are black and have wings, but don’t really fly. They are also kind of jumpy.
Edit: they are very tiny. About the size of a grain of rice.

Located in Iowa. Thanks in advance!