There were a bunch of these shot down just after takeoff, or while on final approach to landing.
They didn't always go so fast that they couldn't be shot down.
Yep! In 1945 they didn't had afterburners. Since the acceleration of those jets was not that great it was no problem for the American Mustangs to f**k those 262s during their starting and landing phase. Therefore the Luftwaffe tried to deal with this threat with piston fighters (espechially Fw 190) to answer the Mustangs.