1. (I don't know, hopefully someone else does)
2. The walk is not "bad" at all in my opinion, but everyone is different. It's a short 1-2 minute walk from any of the DLH Towers to the DLH Security check. Then literally 1 minute walk from security check to the monorail, or 5-10 minute walk from security check to the park entrance. Usually the DLH Security is not too crowded. It can back up at times, but the same can be said for any of the security checkpoints.
3. THe monorail is very convenient both to and from the parks. However, if you are doing EMH or trying to rope drop, taking the monorail is not the best option into the park for that. It is a great option to return to the DLH at the end of the day if you are in Disneyland. Again, probably no more than a 5 minute walk from the monorail to DLH. The ride itself, including loading time, is around 7 minutes.
4. There are movie screenings in the evening at DLH for guests. All the towers have displays on the main level with models, concept art, and memorabilia from the parks that can be fun to check out if you are just looking to stroll around the grounds one evening... perhaps on the way to Trader Sam's. There's a nice fireplace seating area outside Trader Sam's too. Goofy's Kitchen and Steakhouse 55 are both in the DLH. You can grab snacks or food at the Coffee Shop or at Tangaroa Terrace (which also has mobile ordering).
I like the DLH a lot and would recommend it. Of course, I also like GCH a lot too, so you can't really go wrong either way.