Some doubts on terminology
Resistance looking into (the) "X"

Apply a test voltage (say 1V) and measure the test current. The resistance looking into the X is the test voltage divided by the current that flowed. 

Resistance from (the) "X"

I'm not familiar with this usage.

Input impedance (or Thévenin equivalent?)

Same thing as Resistance looking into (the) "X"

Output impedance (also Thévenin equivalent?)

Same thing as the resistance in a thevenin equivalent.