An EK flight number on EK aircraft will get QF points but no QF status credits
A QF flight number on EK aircraft will get QF points and QF status credits

If EK aircraft Dubai DXB will be in the route on/from to Europe.

With most ffp's you can book a ticket for some one else. Your parent can then book a flight for you. No idea is that is part of the EK ffp. One of the few advantages of the QF ffp is that you can move points between family members at nil cost.

If you are collecting from QF F flight's far better to get a AA miles, by a factor of about ~150% to 200%. As sample here. 1 AA mile is worth more than 1 QF point. Getting airline (QF or AA) status may effect that decision. Their are reports on the AA forum of people getting AA miles flying QF flight numbers(codeshares) on EK aircraft. As here in Posts 84 to & 91. But that may be an IT error.