I don't know the specific model you've mentioned , but if your bridge is a Floyd Rose , it's normal ... You should tune it (with a tuner if you got one) few times before they're all in tune , then you lock the strings from the nut.

I don't think that old strings affect each other this way, old strings just have less intonation along the frettboard , that's all .

I think it's the bridge , it might be the tremolo if your bridge is a tremolo type ... If not, I guess you should have a technician to check it out.