The test must be done with the engine hot to gain accurate readings.
Now all your readings are low, but if the system is really rich from the open loop issue, the excess fuel may be 'washing down' the cylinders causing an initally low reading. All of this said it may need the engine, it's hard for me to say over the inter-web, but if those inital compression readings are confirmed, it could be your issue.
Idle at 1000 is alittle high, should be in the 700-800's. Vacuum leaks may be the culprit, check that elbow on the intake manifold as well as the intake gasket itself, they are very bad for leaks.
The small puff of blue smoke would be oil, maybe pcv system problems, pull out the dipstick at warm idle and watch for any signs of smoke, if it puffs like an old steam train, there is excessive crankcase pressure which is more often then not a clogged crankcase ventilation system (pcv), but this can also be tired rings and valve seals/guides over powering even a clean crankcase ventilation system, agian pointing to those low compression readings. Now if the smoke is by chance black its running way to rich (open loop) and may be washing the cylinders down, i would double check the colour of the smoke yourself to be sure.
As far as the jumping back to open loop, I really can't tell without seeing the data steam unfortunatly.
Anyways check for vacuum leaks FIRST, if you cant find any faults and are sure of it, try to find out what the pre-cat readings were, and if they did a cat efficency test before replacing the cat, and is the new cat aftermarket or OEM.
Also Does the car have a secondary air system? and do you know what your fuel pressure reading is?
But again check for vacuum leaks first.
sorry wish i could give you a straight 'do this and it's fixed' kinda answer, but it's impossible without seeing the car, and even then the answers not always so obvious.
Keep us posted and good luck
