To get the marginal distribution of just one rv, you need to sum over the other one.
For example P(Y=0)=P(Y=0 and X=0) + P(Y=0 and X=1)=.4
You are summing over all values of x
P(Y=1)=P(Y=1 and X=0) + P(Y=1 and X=1)=.5
Since these probabilities sum to one
we have .1 left over for P(Y=2)
The last probability, Y=3 & X=1 =>0 should be erased.
Anything that has probably zero shouldn't be listed.
From here you should be able to get Y's mean and variance.
As for the conditional mean of Y when X=1,
you need the distribution of Y when X=1.
You only need these two
Y=0 & X=1 =>0.2
Y=1 & X=1 =>0.3
The correlation between two rvs is the covariance divided by the st deviations
AND by the Cauchy-Schwarz inequality it has to be between -1 and 1.