What's your goal for taking the monorail back and forth to the DLH? If it's just less walking then yes, it will save you some steps. What it probably won't save you is time, especially if you're wanting to stay at the DLH so you can take advantage of early entry. For your strategy of taking the monorail on an EE day, you'll have to be in line at security very early so you can be one of the first through, because if you're not on the first monorail of the day then you'll have to wait for the next one, which will put you in the park late and take up your valuable EE time.
The other thing is that the monorail station is all the way at the back of Tomorrowland. If you're doing Tomorrowland first, that's great, but if you like to do Fantasyland or something else first, it's not quite as convenient and will put you behind all the other guests who are going anywhere other than Tomorrowland as you head wherever else you might be going.
And while taking the monorail back and forth during the day can be nice, you have to remember that the lines can be VERY long, depending on time of year and time of day. They'll definitely be very long at park closing.
Not nearly as much as it used to when it was an hour! I'm not sure it's that much better than doing an "opposite park/opposite day" strategy. It's probably more advantageous for DCA than it is for DL. We almost always stay on-site, but since they changed it to 30 minutes that's mainly because I just like the hotels and the feeling of being immersed in the world. The GCH is my absolute favorite and is so close to the parks. Definitely stay there if you can afford it.