“There are eight persons.” is perfectly correct. No doubt about it!
It's 8 people ?
Correct as well.
But " these are eight people" is a no go.
People is not countable. When the counting is used persons should be used.
Sounds okay to me. If anything, "eight people" sounds more natural than "eight persons."
I'm curious what you're basing this on. See the note here ("Usage") for a summation of the general usage distinction.