1. Which park?
So, you're planning on visiting both parks on the same day? You will need to buy two separate tickets as they don't sell one-day park hoppers (although you can get discounted "evening" tickets for each park at some times during the year).
You will need to start with whichever park has the most in-demand ride that you want to experience. For example, if you really want to go on Toy Story Mania, then you'll need to go to DisneySea first otherwise it is likely that all of the Fast Passes will be taken and the standby line will be extremely long (i.e. 2-3 hours) if you go there second.
Alternatively, if you really want to go on Pooh's Hunny Hunt or Monsters Inc, then it may be best to visit
Disneyland first otherwise the same could happen with either of those rides.
It might be a good idea to check the park opening and closing times as well. I think they're sometimes different (e.g. Disneyland may open 30 minutes before DisneySea). That may impact your decision. The night time show that most interests you may also impact your decision.
If you have been to other Disney theme parks, I would recommend trying to spend as much time as possible at DisneySea at it is entirely unique. So, perhaps start with Disneyland, do everything that you want as soon as possible and then quickly make your way to DisneySea.
2. Character meetings
There are two styles of character meetings - the free roaming kind and the formal "line up and wait" kind.
I'm not aware of any information being published about the times and places for the free roaming characters. The formal character meets all have their times posted (although from memory, they're essentially there all day long). You can ask the cast members about the availability of certain characters, although asking about unfamiliar or unpopular characters may be a little difficult (e.g. I had no issues asking about Donald Duck, but they were less certain about Scrooge McDuck).
The formal character meets have lines. Often very LONG lines. The free roaming characters do not have lines. It depends upon the popularity of the character, but basically a crowd forms and you just have to politely make your way to the front for a photo. There is no pushing or shoving, but you do need to make your presence felt. It's a little confusing as a lot of the local fans seem to like just taking photos of the character by themselves. It can be a bit tricky balancing allowing others a chance to take a photo, while also wanting to step in for a photo with the character. I just try to be quick about it.
3. Fast Pass
I know that the commencement time for Fast Passes is "strictly" enforced (e.g. they wouldn't let us get into line until a couple of minutes before our allotted time). I'm not sure about the closing time. I think it would be relatively strictly enforced because they're very efficient and organised, but they may be a little more accommodating with foreign visitors. I would try to be there within the Fast Pass window to avoid any disappointment.