DLR has a FastPass (FP) system that is very similar to that at WDW. However, it does have some idiosyncrasies that do not exist at WDW that are worth understanding. These two links one of them by me discuss all of the current idiosyncrasies and tricks.
The Joy of FASTPASS - details and secrets:
www.micechat.com/forums/showthread.php?t=5720
Getting the Most Out of FastPass During High Season:
http://mousepad.mouseplanet.com/showthread.php?t=46202 or
www.disboards.com/showthread.php?t=885132
Here is a quick summary of important differences of DLR FP:
1. Enhanced FP This is a relatively recent perk offered by DLR (since 2004, I believe). If you stay at least two nights at one of the DLR hotels and book through AAA you can get EFP. EFP allows you to get FPs more quickly then regular guests. See the Joy of FastPass link above for more information.
2. Expired FPs - It has been DLR policy for a number of years to accept FPs any time that day after the one-hour FP window.
3. Disconnected FP Rides DL and DCA have certain FP rides that are disconnected. This means that when you get a FP for a certain connected ride, the delay until you can get another FP does not apply to the disconnected FP rides. At present there are two at DLR: Roger Rabbit at DL and Grizzly River Run at DCA.
4. FP Initialization for Both Parks The ability to actually get a FP depends on the entrance media being initialized that day when you pass through the park turnstiles. When you do this at either DL or DCA, your entrance media are initialized for both parks at once. This means you can send FP runners to the opposite park you entered to get FPs for the whole group even though no one in the group has actually entered that park on that day.
One other difference from WDW is that DLR does not add artificially long return times at certain parks in the morning. For example, MK always seems to make the first FP return time 10:05AM even those obtained during EMH mornings. DLR does not do this. The first FPs always start the day 40-45 minutes away. And DL does not issue FPs during Early Entry, unlike MK.
I know you are only allowed one fastpass at a time except if you use the tricks. 
If you have a fastpass from Disneyland, can you go to California Adventure and get another? Thanks in advance!!!
The Fast Passes in Disneyland and California Adventure are not connected to each other. SO you could grab your favorite FP in Disneyland, plus one for Roger Rabbit since it's disconnected from the system, then head over to DCA and grab you favorite FP, and one for Grizzly River Run since it is disconnected from DCA's system.
