"Split Stay" is an informal internet term and not an official description of back to back stays at DW so to Disney you would be booking two completely separate reservations. As they are going to be treated as two separate reservations you will have a second deposit, two reservation numbers and two separate 180 days for booking dining reservations. The actual process of booking two resorts is no different than booking two separate stays.
It's usually not practical to get
free dining for both stays since it would require a second set of tickets and room at rack rate. Instead look into booking WL with a room discount. If you really want a paid dining plan for the WL days you can book a ticketless package, but it can only be done on the phone. All the rules of a package apply ($200 deposit, final payment due date, penalties and fees for changes within 30 days of arrival), but you could see if a room rate discount is available.
As far as the logistics of transferring your luggage from WL to AKL that is easy. You can call bell services and have them transfer your luggage, but it usually doesn't arrive at the new resort until late afternoon so anything you need you should keep with you for the day. Or, you can drive or take a taxi or uber to AKL with your luggage and check in. If your room isn't ready you can store your luggage with bell services at AKL. Whether transferring your luggage with bell services or by yourself, you will need to call when you are in your room at AKL to have the luggage delivered.
Your free dining will only apply to the AKL stay and can only be used beginning with the first day of the AKL stay. If you decide to book WL for the first few days of your stay, your park tickets will be attached to the AKL stay. You will be able to pick up your tickets up to 10 days early, but will not be able to make FP+ reservations for those days until you arrive and actually activate the tickets.
Another option is to book the free dining package for the WL stay since that will be at the beginning of your vacation. Include tickets that will cover the entire stay at both resorts. This way you will be able to book FP+ for your entire trip at the 60 day mark. The dining credits will be good through 11:59 PM on your WL check out/AKL check in day. Book the AKL as a room only reservation and pay out of pocket for food or book a ticketless package with a paid dining plan if you want a dining plan for the AKL part of the stay.