Too much light (bright) depends on the cave. There is NEVER such a thing as too many lights. Until I switched everything to LEDs I had usually 14 lights in my cave pack. Sure some were pretty small weak lights. The NSS recommends 3 sources of light and most cavers will always have at least 3. If not LED, have spare bulbs. Also have enough batteries for your main light (headlamp) to last 3 times the planned length of the trip, assuming this is a wild cave. A typical rescue takes 5-12 hours to get setup and start moving in. Add to that the amount of time you will have to wait until you are missed and you get the picture.
Having lights that will step down are great. I cave with a PT Apex and use my P3D to spot things. Both can be fairly dim and then step up to spot ceilings or formations. Don't shine the light into peoples eyes, if using a headlamp don't look directly at them or you will be shining the lamp into their eyes.
A helmet is HIGHLY recommended. Cleaning blood and hair from the ceiling of a cave is pretty annoying.
As far as animals you could see snakes in the entrance area. In the dark zone you are most likely to see crickets, salamanders, small stuff, and of course bats. The light shouldn't affect them much. I was once in a tour cave and the guide told the crowd that LEDs are no good for caving for several reasons. First they aren't bright enough, and second pulsing of the light confuses the bats. Funny thing that same summer a big topic at the NSS convention was the PT Apex and the Stenlights as being the new standard in cave lights. I want to go back and find the guy and compare his maglight to my P3D.
Anyway bring all the lights you want. Just remember you have to carry them. You will want at least 1 head mounted light so your hands can be free to help you navigate the cave.
Any other questions PM me.