I have never seen "businesspersons" before, this might be the first stage of a new word in the English language! The word "businessmen" is very common, and the author probably wants to be modern and gender neutral, so he makes up "businesspersons". Perhaps it will become a common word in the future. Another example: "the chairperson" (or just "the chair") is now quite common to hear, instead of "chairman". I expect "chairperson" looked strange the first time it was written. The problem here is that native speakers can make up new words (how exciting, how modern!) but language learners cannot (oh, your English is wrong!) :-) Regarding "people" vs "persons": We nearly always say "people" and not "persons" - you have learnt correctly. "persons" is usually only in very formal (especially legal) contexts. e.g. "Companies are legal persons and can enter into contracts with other legal persons." "Persons found trespassing will be prosecuted" I only write this at work (in law), never in everyday life. In this case, I think the author is simply converting "man" to "person" to convert an existing English word into a more modern one.

Quick answer: 1) It is acceptable. 2) "businesspeople" is a safer choice. 3) In all such situations, when in doubt I try to dodge the issue completely. In this case, two possible suggestions are "entrepreneurs" and "business owners." "Entrepreneurs" is somewhat complimentary; "business owners" is somewhat plain and factual. Speaking as an elderly US native speaker, it sounds "unusual" to me. That means it attracts attention ("Oh, look, she's being gender-neutral") which is exactly what you don't want. On a quick check, the American Heritage Dictionary online has entry for "businessperson" but it just doesn't say what the plural should be, and has no entry for "businesspeople." Merriam-Webster has an entry for "businesspeople" and cites first known use in 1827; I find nothing for "businesspersons." Another quick check, although such counts are not reliable: Google is showing me 3 million hits on "businesspersons" and 52 million for "businesspeople." When I say it's acceptable, what I mean is that no ordinary native speaker is going to feel sure that it's wrong, and nobody reasonable will complain.