1) Only Magicband+ works, not legacy Magicbands. Even still, you currently cannot charge to your Magicband+ nor open your hotel room at DLR (functionality to come later). You can currently scan into the parks and Lighning Lane, and scan for Photopass photographers. The bands also light up on certain rides and during nighttime entertainment.
2) Yes, there is a 30 minute early entry every day at each park for on site hotel guests. You can only choose one park to start at. The parks typically open at 8:00, so early entry starts at 7:30. You will want to be lined up from the Grand Californian at the Downtown Disney security entrance around 6:30. There are typically not dedicated park entry lines into
Disneyland for just early entry, but you will be directed to the right inside the park towards Tomorrowland. Only Tomorrowland and Fantasyland are open during early entry. Most people here recommend heading towards Fantasyland, which consists of mostly non-
Genie+ attractions. I highly recommend spending your early entry at DL, as there's simply more to do there. You also would have the opportunity to head towards Rise of the Resistance or Mickey and Minnie's Runaway Railway at park open, both are Individual Lightning Lane attractions. Park hopping will be allowed by September beginning at 11:00 am. The parks are literally 3 minutes apart from each other and very easy to go back and forth, and you can book LL for the other park after the hopping time. You also will need to keep your eye on the entertainment schedule and park hours, which are released about 6 weeks out. During September, Oogie Boogie Bash will have started on several nights per week, which is Disneyland's equivalent to Mickey's Not So Scary. OBB takes place at California Adventure and closes that park early several nights per week, and also severely impacts crowd flow and patterns. If there's an OBB on the day you attend, then Disneyland will be packed that night.
3) No, you cannot get through both parks in one day using Genie+ as a first time visitor. You could decide to hit only highlights in each park, but I'd advise against that for a first time one day only visit. My first recommendation is to spend at least 2 days at Disneyland Resort with park hoppers. If that's not possible and you only have one day, I recommend spending it only at Disneyland. It's the original park, it has so much to do, and there are a lot of unique attractions there. I recommend looking through a list of attractions at DL so you get a sense of what there is to see, and keep in mind that even some of the "same" rides at DL compared to WDW are very different. For example, Pirates is far longer and more elaborate at DL. Also, when you go in September, it's likely that Haunted Mansion will be Haunted Mansion Holiday, which is a totally unique experience. If you must go to DCA, then make sure you plan what rides are your highest priority there. I would recommend Radiator Springs Racers, Guardians of the Galaxy, and Webslingers at DCA.
4) If you stay until Disneyland closes, which is typically midnight on weekends, then you probably would only need 1 hour to get to LAX. Keep in mind Disneyland is typically open 8:00 am - Midnight on weekends year round, with the 7:30 am early entry every day for on site guests. If nighttime entertainment is important to you, Saturday will offer an opportunity for fireworks, but Monday in September might not. Wind often cancels fireworks at DL at the last minute. World of Color at California Adventure takes place nightly year round, with the caveat about the park closing early to day guests for OBB.