Can an EWG behave as an EDG and vice versa? Can an Electron Withdrawing Group(EWG)(like NO2, F, Cl, OH, etc.) behave as a Electron Donating group(EDG) in a compound where a carbocation is present in order to stabilise it?

Does the position where it is present or distance from the carbocation affect it's behaviour as an EWG or EDG?

I feel that it should behave as an EDG as carbocation is electron deficient so it has a greater tendency to accept an electron. 

Can we say a similar thing that an EDG behaves as an EWG in presence of carbanion as it has excess electrons?
Of course not. That's why it is called EDG or EWG. It tends to destabilize it more in the absence of other effects like resonance and hyperconjugation.