Hi. First, my apologies for not being able to post directly to the link where this info is. Some rule here about needing a post count higher than 10 before being able to post a link. I understand why, just doesn't help here. Can someone else please post the link to the POP Century FAQ thread in the Resort forum here? Specifically post #4 is all about transportation.
Here is some info from that thread that should help you:
Pop Century bus hours of operation
begins one hour before park opens, including park Early Magical Hours
begins 30 minutes prior to first scheduled on-property character breakfast
approximately one hour past parks closure; keep in mind that this is a very busy time for transportation needs, so waiting times and commute times can be greater
Routes to get to popular resort Character Breakfasts from Pop Century.
Chef Mickeys at Contemporary Resort (bus to Magic Kingdom then Monorail to Contemporary (or walk)
Ohana Breakfast at Polynesian Resort (bus to Magic Kingdom then Monorail or boat to Poly)
1900 Park Fare at Grand Floridian Resort (bus to Magic Kingdom then Monorail or boat to Grand Floridian)
Cape May Café at Beach Club Resort (Best option cab; or bus to Disney Hollywood Studios then walk or take a boat to Beach Club Resort)
Routes to get to Dinner Shows from Pop Century
Hoop-Dee-Doo Musical Revue at Fort Wilderness (bus to Magic Kingdom then boat to Fort Wilderness)
Polynesian Spirit of Aloha Luau at Polynesian Resort (bus to Magic Kingdom then Monorail or boat to Poly)
As for your specific questions, I would recommend a 9am/9:15am departure from POP to the TTC, then monorail over to the Contemporary.
And yes, you should be able to do AK straight to DD, then DD to POP later. Someone will correct me if there is not an AK to DD direct bus, but I believe there is. Worst case, just go back to POP, drop off your stuff from AK, rest for a bit and then head over to DD. That little refresh stop may make the world of difference after a day at AK.
Have a great time.