Car cutting out and not responding.

You have an intermittent electrical connection problem as evidenced by the clock losing its memory and resetting. There's two common possibilities. One is you have a battery cable clamp that is loose or has corrosion inside that wasn't cleaned off when you reinstalled it. The other is related and could have been about to occur even without the battery replacement. Follow the smaller battery positive wire to the under-hood fuse box and be sure that connection is clean and tight. Also follow the smaller negative wire to the body and check that one.

The Engine Computer runs a number of self-tests that, if passed, reduce the number of tests the emissions tester has to perform. There is always a long list of conditions that must be met for those tests to run, called a "drive cycle". Some of those tests may take days or weeks to run and pass. You won't meet all the conditions for all of the various tests to run in a few miles.

Every time that electrical connection acts up it will cause the stored self-test data to be erased. You did the same thing when you disconnected the battery. Someone at the dealership should be able to describe what you need to do for the self-tests to run. It can involve a number of things including engine up to a certain temperature, a brief spurt of wide-open-throttle, prolonged steady driving above perhaps 45 miles per hour, and an abnormally long period of coasting.