Saturn has being running awful since oil change (my son-in-law change it)

My son-in-law wanted to be of use, and said he could change the oil in my 2006 Saturn
VUE (6 cylinder). Well, he drained the oil out of the pan on the bottom of the car (a
important pan in oil - not a place he should have taken out), and didn't change the filter.
The car has not run well since. (This did occur of a cold winter snap of air.) A friend told
us that the car was filled to over a quart of oil and that the transmission fluid was down.
Said to change the oil again with a filter, and add just a little to the transmission fluid.
He also said the low state of the transmission fluid was causing the problem due to the
below 30 degree weather.

So..car was running fine before the oil change. Now it won't go into gear unless we shift
the automatic to a gear and hear it klick. Also, the RPM is running up to 4 to change a
gear (I don't mean we have a straight shift, I mean from 1 to 2 in the automatic). Also,
some times it while 'lose' the gear it is in, while you are on the road. We have to stop
the car, restart, and listen for the click again. AUGHHHHH!

Is any of this true? Or do I have a real problem with the Saturn now? My son-in-law
swears he did not touch anything on the car.

Thank you so much!