Just to start you :
1- No idea what you're precisely asked.
2- T = max{X1...Xn}
P ( 0<T<A) = ( A / thêta ) ^ n
since we need all X1 ... Xn to be smaller than thêta for their max to be smaller than thêta.
Hence : P ( 0<T<A ) = Integral ( t=0 to A ; f(t).dt )
with f(t) = n*t^(n-1) / (thêta^n)
E(T) = Integral ( t=0 to thêta ; t*f(t).dt ) = ... easy calculations ... = n*thêta / (n+1)
I suppose your constant c should be c = (n+1) / (2n)
such that E(U) = c*E(T) = thêta / 2
V(U) = c² * V(T) = ... not so hard calculations ... = thêta² * n / [ (n+1)² * (n+2) ]
but you will need help from another one with Cramer-Rao bound
