In one query (Q1) we will have an input variable that we wil record in a Z table.
What do you mean by this? Are you running any APD based on Q1 to write to ZTable?
Suppose if Q2 runs first, what value it is picking from ZTable? How does your web template result looks like if Queries execute in unwanted sequence?
Did you take trace to know which one is executing first?
There is no standard setting to execute the sequence. If you want Q2 to take variable value of Q1, you can simply use replacement path by Q1 variable. This does not require Ztable concept at all..