T-test question question, following, different

dvilayphet

I have the following queries on the t-test,

1) Why with sample correlation the t-test formula is different from what we saw in Level-1 t-test formula? As we know, in Level-1 the t-test formula was (estimated value - hyphotesized values)/ std. error

2) Why with sample correlation the DF is n-2 here, while in Level-1 formula it was n-1?

3) Why DF is included in the formula itself here while in Level-1 we had to look up DF in the t Table?

Apprecite if someone can clarify. Many thanks in advance.