1. Usually before the standard dinner time (18:00-19:00) or afterwards.
There is no evening parade this Christmas season, the normally daily Disney Magic On Parade will be cancelled.
There will be the Christmas Cavalcade (which is just a 5 minute small parade) that will run about 5 times during the day.
Also there will be the Princess Promenade (which is also just a 5 minute small parade) which will run once at the beginning of the day.
There are no meets with any of the characters available after these mini-parades.
In the evening there is the Castle Lighting Ceremony, the Tree Lighting Ceremony and Disney Dreams of Christmas.
2. In the main Disneyland Park the answer unfortunately is no. A couple of years ago there was always a big outside disco.
With a DJ and some characters, this started at 22:00 and ran until 23:50. Usually in between also the Fantillusion Parade. Then at midnight there was the countdown with a big fireworks display. And afterwards again the disco until about 01:30.
However, starting NYE 2012-2013 they completely changed it. No nighttime parade, no disco, no nothing. Not even an actual fireworks display. Just and extra showing of Disney Dreams at midnight. They started focussing more on the extremely expensive NYE dinners at the hotels, which (even with this ridiculous price) still turned out to be really popular. There is some small entertainment at Disney Village and a so called "Video Dance Party" at the Walt Disney Studios Park (a small stage in front of the Rock 'n Roller Coaster with a screen where they play MTV videoclips, and on stage there are some dancers just dancing along with the videos. The crowd can dance along with if they want, that's it). But that is basically it.
To be honest, I've experienced NYE for many years in a row, and last year was my last in a while. I'm not doing it anymore until something changes. The Video Dance Party is just a mess, the entertainment in Village is barely nothing and in the Disneyland Park they don't even do anything anymore! To me, it's not worth it any longer.
Yes, the rides are open. But do expect EXTREME queues. And when I say extreme I do mean extreme. Queues up until about 4 hours are pretty normal for a night like that.
3. Yes, the Princess Pavillion is a walk in attraction, sort of. You have to get a reservation ticket at the Old Mill, this is completely free and can be purchased at the beginning of each day. On that ticket there are two times, and a half hour limit between them. So for example 11:00 and 11:30. This means that within that half hour you can go into the actual Princess Pavillion queue. Honestly, I reckon the queues for both the ticket and the actual entering of the Pavillion are going to be massive. Normally you queue up, and at the very well end of it you find out which Princess you get to meet. There are always two princesses, and at the end of the queue the Cast Member either tells you to go left or to go right and then you're with the Princess. This cannot be requested, you can't give your preference. However this Christmas season all the princesses are being axed from the Pavillion. You can't meet them, they will only appear in the Princess Promenade. The reason for this is that Anna and Elsa from Frozen will be taking their spots. Those two will be the only onces at the Pavillion this entire Christmas Season. And since their popularity is pretty much absolutely crazy, I reckon the queues are going to be absolutely massive. Especially during the most busy two weeks of the entire year. There's also going to be Merida, she will be meeting at Casey's Corner but again, same story. Expect massive queues.