How do I find the effective resistance of a Thevenin circuit if the points are in between resistors
For thevenin resistance-
In  2nd fig. ,
4ohm resistor is shorted so remove it and you'll get 1ohm parllel to 2ohm so equivalent resistance would be 2/3ohm and that is thevenin resistance
For maximum power -
there are 2-3different methods but
You can  connect  a resistor of value equal to thevenin resistance (2/3)  between point a and b (in 1st fig.) And calculate current through that resistor and then you can calculate power by formula P = I² × R.

direction and value of current can be found using  mesh,nodal , superposition theorem whatever you like you can use to calculate it