1. Yes, Just like push/pull/slide someone over a cliff, the same applies here. If it is a beach or river bank then they get wet. If it is a dock or cliff then they fall (save if applicable), then get wet. See below.
1a. That would be up to the creature and any other affects on the creature, but I would say they fly. See below.
2. No, and Yes See below.
3. No, see below.
4. Yes (sort of), see below.
Rules from DDI
Slide: PHB1 pg285; MM1 pg283 - When you slide a creature, there’s no restriction on the direction you can move it.
Pull: PHB1 pg285; MM1 pg282 - When you pull a creature, each square you move it must bring it nearer to you.
Push: PHB1 pg285; MM1 pg282 - When you push a creature, each square you move it must place it farther away from you.
Forced Movement: PHB1 pg285; MM1 pg311
Movement that a creature is compelled to do, specifically a pull, a push, or a slide. A creature can be moved in other ways, such as through teleportation, but only pulls, pushes, and slides are technically forced movement.
Two-Dimensional: Forced movement is normally two-dimensional; all the squares of the movement must be on the same horizontal plane. Forced movement can become three-dimensional when the target is flying, is moved through a substance such as water, or is on a non-horizontal surface, such as an incline, that supports it. This means an earthbound target cannot normally be pushed to a square in the air, but a hovering target can be. Similarly, a target can be pulled down a flight of stairs, and it can be slid in any direction underwater.
Best Answer
The overland movement rules apply to flying as well as to land movement, so it is possible to fatigue yourself by flying too much. There are not any rules for flying being more tiring than walking, however. Also, there’s nothing about hovering (or treading water, for that matter) causing fatigue; all the rules for getting tired while moving focus on movement so if you don’t change position they don’t (obviously) apply.
A few specific creatures have rules limiting their flight to certain durations after which they’re required to land. This is relatively rare, however, and almost entirely found on player-focused material since the game rarely has monsters “on screen” long enough for it to be relevant.