In your experience, is there enough time to go across Mary's bridge during the 1.5 hours between the two castle tours? I am looking at the map provided at http://www.hohenschwangau.de/837.html. I guess the route to be able to go to the bridge would be to take the yellow dotted line from Hohenschwangau Castle (20 minutes) then connect to that pink dotted line to get to Hotel Lisl to catch the bus. Is the pink dotted line about 10 minutes?
Yes.
Depends on how fast you walk and how many cats you're herding. It is a pleasant though steep walk up to Neuschwanstein. Not everyone can get there that fast, IMHO. You can always see the bridge afterwards, though, so no worries.
We did Hohenschwangau first, then took the bus to the top of the hill. From the bus stop walk uphill a short distance to the bridge, then back down hill to Neushwanstein. An hour and a half is plenty for that but probably not if you walk up the hill rather than take the bus.
Yes, as long as you are an energetic walker and don't walk beyond the bridge. As I recall, it's only about a 10-minute walk beyond the "castle", so you only need about 25 minutes to do it (10+5 minutes there +10back). However, if the time is tight, try to do it after. If you are still feeling energetic, you can keep walking up the hillside beyond the bridge. After about 30 minutes, you will come upon some access points on your left for tremendous views above the castle and overlooking the entire region. 30 minutes back down, too, of course...