I saw it when I was probably 4 or 5? I had recurring nightmares for YEARS. Like, well into my mid teens. I'm pretty sure I even had one or two as an adult. I'm recovered now and I've watched the movie without incident, but I don't like it and I don't really want to willingly watch it again.
That's a good question. If I'm honest I haven't seen UT in probably 15 years.
I think it was the cornfield chasing parts? I also recall just being super creeped out by E.T. himself. The way he made sounds, the way his fingers move, etc.
The biohazard stuff you're talking about scared me, but I think just the sounds E.T. was making, not the guys in suits specifically.