1. Is it legal for F2 visa holders to use eBay to sell things? Not comercially, just selling unwanted household items..

2. Is it legal for F2 visa holders to receive payments via Paypal?
(By payments I mean both payments from eBay buyers and 'personal payments' like money sent from friends/family members.)
If yes, is it legal to withdraw the fund in the Paypal account to a US bank account?
If no, is it legal to use international/home country Paypal account?

3. Is it actually legal for F2 visa holders to receive payments to their bank accounts?
I know employment/payroll is not allowed, but does that mean they are not allowed to receive any kind of payments/checks at al

F2 visa holder, like F1 visa holder is exempt from residency. You are not allowed to work.
Yes, you can have PayPal account and eBay account as long as it is not business related activity.

The issue here is the proof that it is not a business, the number of items sold, the type of items sold, obviously they would be used items they owned and would show a pattern of being merely the sell off personal items

Cinchan:

If all of your transactions are personal in nature, they are permitted, as is receipt of the payments via PayPal.

As Fr Chuck noted, you will get into trouble only if the pattern of your transactions clearly shows you are engaged in a business. To do that, you would have to show sales on a regular basis throughout the year.