Can someone explain how to know what to use where?
Is it always the case where whether it’s with T-stat or F-stat, you reject H0 if calculated stat > critical value or calculated stat < - critical value?
Yes.
Reject H0 if H1 passes level of significance. You may test it via T-Stat or just read probability significance level if it is given. Eg. if you test with 95 % significance, probabilitiy p-value level should be less than 0.05 to reject H0 and accept H1.
Yes, it is.
It is best to understand the reasoning behind it rather than remember it like this.
If you have doubt on the reasoning, perhaps you could clear it here.