No idea if RO is proposing paid upgrades at OLCI.
As a ST E+, you can guest one person in the lounge. Other persons may pay for their access if space is available. You won't use the 2F lounge. In fact 2F is only for check-in and, as Romania is not part of the Schengen area, once past security in 2F, you will be directed to Terminal 2E- concourse L. It will be the AF lounge in 2E-L that you'll use. It's a very nice lounge. Paid access is 75€ for adults and 35€ for children. Your 2 y.o. child should of course enter for free.
If you upgrade to C some pax, those ones will have free lounge access.