A couple of quick thoughts for
@Ziggie
First of all, don't worry about having an HA room if you don't need one. Typically, you'll know if you need one. If you can (safely) get in and out of the shower, and don't need grab bars in the shower or next to the toilet, you should be fine.
Regarding the size of the ECV - talk with your rental company, and let them know about your plan - they can advise you best on which scooter to rent in your specific situation. I'm an expert on my personal ECV that I own, but I couldn't tell you a single thing about any scooter other than mine outside of generalities.
Next, do keep your ECV in your room overnight, when charging. For lots of reasons... not the least of which is that you don't want someone messing around with the equipment that is your "legs".
You got some really good advice re: the backpack in lieu of a rear basket. Resist the urge to make your ECV into a pack-mule; it's so easy to drag along extra "stuff" when you think "Oh well, I'll just throw that on the scooter too..." Not to mention the fact that I hate spending my Park time at bag check with security! They are super nice people, but I'm at WDW to play!
As far as transportation goes, you probably have seen in the past how the buses will work - you will load the ECV first, but get off last. Your family will board with you. It's easy, just drive straight up the center of the ramp, and don't turn until you are at the very top - and take your cues from the driver.
Monorails have portable ramps to bridge the space between the platform and the car. You will see those same portable ramps in use on many of the other boats at WDW - especially the boats around HS, Epcot and Disney Springs. The only places you will have an issue with boats are some of the smaller launches where you have to step down into the boat. Those can't take your ECV. All of the other boats at WDW are fine.
Yes, you will have to watch out for people darting out in front of you - little kids, morons who can't keep their face out of their phones, and the self-absorbed selfie-takers. But here's a little secret for you: You have to watch out for those same people if you walk, or if you use a mobility device. Don't let that freak you out. Take a few minutes to practice - really practice! with your rental unit before you take off for the parks, and get a good feel for how it turns, how it stops, how it handles in general. Remember that you need to cross the tracks embedded in Main Street in the Magic Kingdom at an angle. And if you can, have someone "flank" you on either side, (or front and back, if you prefer) to help create a buffer if needed.
Don't worry - I have been using an ECV at WDW for a lot longer than I would like, and generally speaking, it's SO much easier now than it was even 5 years ago.
I hope your trip is everything you want it to be!