Yes. the conditional expectation of X given Y is simply the expectation of X if X and Y are uncorrelated. This is a consequence of one of the properties of conditional expectation.

the statistically independent random variables are uncorrelated but the converse is not true ,i want a counter example,

If I have two source of noise let as say two laser diodes so the pink noise that generate fro both of them is it correlated or uncorrelated

to convert raw data of correlated variables to data matrix of uncorrelated variables (Principal Component)

Yes it is. That is actually true for all random vars, assuming the covariance of the two random vars is zero (they are uncorrelated).