Are you using the button on the end of the wiper stalk to switch on the auto wipers? One push (upwards) of the whole wiper arm should put the wipers on continuous low speed, not auto. The test is if the auto wiper symbol appears ion the bottom right corner of the tacho display. If it does, is there some muck over the sensor under the windscreen behind the rear-view mirror? If so, clean the screen and see if that fixes it. But if the wipers go intermittent when stationary, that sounds like they are on continuous, as that is how they are set up to behave.
Stop-start is quite likely to not work on an old battery that only does town driving. The battery needs to be well-charged for the stop-start to work and the garage may have charged the battery before selling the car. The test is whether the stop-start works after you have driven a decent distance (say, 10 miles+) at motorway/main road speeds. If it does, that explains the problem - it's not economic to replace the battery just to get the stop-start to work, so just consider the stop-start as a sophisticated battery condition test!