What are the visa rules for a child accompanying a parent with a business visa in Thailand?

Once you get any type of multiple-entry visa, no fee on each entry.

30 days extension is available for only entries on visa-exempt or tourist visa entry.

1. when she comes back to thailand to gain another 90 days, is there any fees to pay?

-> no fee

2. she wants to travel with her baby 1 y.o., can the baby apply for non-o using the same business invitation letter?

-> You need to check with the embassy where she would apply for her visa. If her Non-B is for business, not for employment, I don't think many embassies issue Non-O dependent for a foreigner who stays in Thailand legally with that type of Non-B.

If the embassy issues Non-O dependent in that case, you need far more documents than just a business invitation letter.

3. if the baby get TR 60 days multiple entries, later get extension 30 days, leaving 90 days, will the baby get 60 days when coming back to thailand on arrival? Is there any fees to pay to get these 60 days?

-> will be stamped for 60 days as long as entering during that Multiple Entry Tourist Visa is valid. No fee for entry on a valid tourist visa.

4. how many times in one year calendar can you extend +30 days at immigration bureau in Thailand?

-> no limit on the number of tourism extensions per year. But you can apply for a 30 days tourism extension only ONCE per entry on a visa-exempt or tourist visa.

BTW, minors under 15 yo is not penalised or fined for overstaying. But overstay is overstay even if it's a newborn baby. It's the baby's parent/guardian's decision if she wants to have her baby overstay or let her stay in Thailand legally with a proper visa or way.