I visit often enough that I just drive to the self parking lot and tell them I am checking into the Grand. They just let me through without checking anything. It's directly across the street from the Grand.
You can do online check in 5 days before check in date. The room is often ready early when I do that. You'll be able to enter DCA from the hotel entrance if you want to do that. And, yes, if you want to carry your stuff to the park you can. You can also check any bags with Bell Services in the lobby and then either pick up your bags on the way to the room later or have them delivered to your room. You do have to be in the room for the delivery.
There are resort activities and you can get the info sheet from the front desk. You can participate in all 3 hotel offerings. Depending on what day you are staying, you might be able to take a tour of the hotel or of the
Disneyland hotel. The Disneyland hotel tour is offered on Saturday and was very nostalgic (I loved it) when I took it.
If you want to take any of the fitness classes, those are booked through the spa and you'll need to book in advance as they fill up. Some are only available to resort guests.
Room service is available and the menu is somewhat different than the restaurants onsite. They also have door hangers if you want to pre-order breakfast for delivery in the morning. I think it has to be on the door by 11pm or midnight.