Incorrect

P(X2=0)=7/12 is false

P(X2=0|X1=0)=7/12

while P(X2=0)=8/13.

It doesn't matter when you select.

If you don't have any info on the first selection the probability is the same.

The probability that the first card from a deck is the ace of spades is 1/52.

The probability that the tenth card is the aces of spades is also 1/52.

If you give me some info on the first nine cards, then the probability changes.

So P(X_1=0, X_2=0)=P(X_2=0|X_1=0)P(X_1=0)= (7/12)(8/13)

In general

P(X_1=a, X_2=b)=P(X_2=b|X_1=a)P(X_1=a).