The first question is when in May are you going? There is a big difference in terms of crowds, operating hours, and entertainment schedules from before and after Memorial Day weekend. Memorial Day weekend (starting that Friday), has generally been the kickoff to the summer season. For the last few years, they've had a 24-hour day (i.e., open at 6:00 am on Friday and close at 6:00 am on Saturday) on the Friday before Memorial Day. Last year, it was a zoo in the parks. The year before (2014) wasn't so bad. No one knows what 2016 will be like (or if they'll even have another 24-hour day). Prior to that Friday, the parks are usually operating on shorter hours and with reduced entertainment (on weekdays at least, Mon-Thu). Weekend (Fri to Sun) hours and entertainment tend to be longer (more like summer or other peak periods).
I know you don't have to make FPs in advance and dining reservations open up 60(?) days in advance but aside from that I don't even know where to start!
Disneyland Dining reservations open up 60-days in advance, but generally do not fill up super quickly. You can make them online or over the phone. The online system rolls somewhere between midnight and 6:00 am. The phone lines open up between 7:00 am and 8:00 am, but note that if you call on the 60-day mark and there is no availability, it probably means they haven't loaded it into the system yet (it happens fairly often).
Operating hours are generally announced 45-days/6-weeks in advance and entertainment schedules are often not posted until around the 30-day (or less) mark.
It will just be my husband and I (21) and we can last from sun-up to sun-down. We really just want to focus on the rides and entertainment because we can see the characters in DW. How many days would you allow and would you recommend hoppers or just stick to one park a day?
When you say "sun-up to sun-down" do you mean from park opening to close? I think most folks need 5-days if they really want to do everything (or almost everything) at a fairly relaxed pace. You can probably squeeze a lot into three-days, but it will mean giving up some things. I highly recommend getting park hoppers. DL and DCA are only 110 yards apart; you can see into the parks from each other. To put it in WDW terms, think of DL like Epcot's FW, DCA like Epcot's WS, the Esplanade is like the bridge that connects FW and SW, and DTD would be just outside of International Gateway. It makes park hopping very easy and can be very beneficial, especially when DL remains open later than DCA (often by an hour or so).
In terms of characters, yes, there are overlaps between the two resorts, but DL does have some unique characters (or characters in unique outfits). Everything is subject to change, but if you were going soon, you might see Oswald, Mary Poppins and Bert, Captain Hook, Cruella de Vil, Fairy Godmother, McQueen, Mater, Red, Olaf, Russell, the Mad Hatter, the Evil Queen, and the Fab Five in their 60th Anniversary attire. You wouldn't necessarily find them out and about at WDW on a daily (or fairly frequent) basis.
Someone told me Fantasmic fills up quickly and recommended getting a dining package with it. Yes? No?
Fantasmic, along with the Rivers of America, will be closed starting on January 11th. The re-opening date hasn't been announced, but DLR has been saying they'll be closed for at least a year. So, most likely, there will be no F! in May of 2016.
Any amazing restaurants we should try out or certain experiences we should make sure to catch?
For dining, my favorites are Cafe Orleans (DL), Carnation Cafe (DL), Blue Bayou (DL), Carthay Circle (DCA), Storytellers (GCH), PCH Grill (dinner, PPH) and Ralph Brennan's Jazz Kitchen (DTD). There are also several good QS options (French Market and Plaza Inn).
It sounds like you've been to WDW. If you have, I highly recommend taking a look at
HydroGuy'sA DLR Guide for WDW Vets. It'll help give you a sense of the similarities and differences between the two resorts.