I think the RoC flag is good as it is.
It's well known, especially in Europe, but also elsewhere.
It has no Greek and no Turkish attributes. It's 100% Cypriot!
It was even designed by a TC so no one can say it's associated with GC's only.
Someone who hasn't seen the flag before would instantly know it's the flag of Cyprus... if they have half of a brain that is... or at least browsed a world atlas once.
Personally I think the design is beautiful. It's simple but effective.
As far as a new national anthem goes I think it should be something newly composed. Perhaps a collaboration between a GC and a TC? Lyrics in English sounds like a good idea since it most likely will be the language spoken between GC's and TC's... especially the younger generation... and the future of Cyprus belongs to them. However, I think the chorus/refrain should contain the words Kypros and Kibris. Perhaps once phrase describing the love of Cyprus repeated in the two languages (Cypriot Greek and Cypriot Turkish).
Just my €0.02.