1. Yes, there are lockers at the station, at platform 1.
2. Nearest stop from tourist information is Schranne.
3. Walking in Bamberg is generally nice, but the station is not in the most beautiful part. It is totally safe but the walk to tourist information is not very idyllic until you cross the canal.
4. Only with town busses you have to change lines to get there, not with regional busses which are even faster but not run as frequently as town busses. You could take busses 978, 983, 989, 991 e.g.
5. There are two bus stops at Bamberg station which can be quite confusing! Regional busses stop directly at the forecourt of the station building - another plus of them. For town busses, if you come out of the station you have to cross the traffic lights and then turn to the right into Ludwigstraße and walk 50m.