#1
When I strum the E and the A strings of my guitar (Squire Strat (unplugged) it makes a weird rambling/buzzing sound. Does anybody knows whats wrong?

Are the pickups needed to be replaced?
Are the strings needed to be replaced? -> (like 3 months old)

I'm really carefull with my guitar, it always stands on its place and there's no cold or something in the room.
#2
If it's unplugged, that means no sound is coming out other than the strings, so it's not the pickups. It could be your action. Squier's a bit ****ty anyway, so it could just be the guitar. And yes, replace your three-month old strings before they turn black and break and stab you in the eye >.>