Yes, the mean PE will be half of the maximum , but not just like that.
PE at any instant is 1/2 kx2 = 1/2kx02cos2(ωt+ø) ,
avg. of cos2(ωt+ø) over a time period is 1/2.
No. It would mean (A parallel C) in series with (B parallel D). Calculate the current through the resistors and from this you can find the current through the bridge.