The Tiki House and Tom Sawyer's Island usually close at dark. Actually, I think TS always closes at dark. Disney is adding a night safari, but in my experience the AK safari ride always closes at 5pm. Lesser rides are not always open for EMH.
ANY ride can go down temporarily during ANY day. Over the years we've seen a number of rides go down, and heard of many more. all it takes is one really dumb guest doing something really dumb to gum up the works. A few of the biggest rides go down like that, well, it isn't uncommon: Space Mtn, RNRC, Splash. Test TRack went dow quit a bit when it was new, but is now pretty reliable. Others we've seen down: BTMRR, POTC, HM, PPan, 7D, TSMM, Star Tours, Buzz, EE, Dinosaur, Primeval Whirl, M:Space, Energy, Mexico, safari, Kali. Oh, the monorail many times! Also the shuttle boats!
In half of AK park and all WET rides close during a severe thunder storm. All the animal attractions, Kali, and EE. Expect similar at Universal.
For Epcot, the hours of each half are listed. Often the WS opens at 11am-9pm, and Future World is open 9am-7pm, except big rides like Soarin' and Test Track will stay open past 7pm.
Oh, except there are often rehabs- like the current one of Soarin' that can also close rides.
I suppose the best approach is patience, doing a bit of homework (for major announced rehabs), and maybe the new app If you wish. the new app tells you if a ride is down (very temp few hour kind)...though if you happen to be at the entrance of a major ride JUST when it re-opens! BONUS! Well...that is, if you are brave enough to be the first one back on a ride that was JUST shut down for some unknown reason.
Characters are another matter. We don't usually scope out characters. We only see them if we happen across a short-ish line. It used to be that at busy times WDW offered po up unannounced characters. I think those are kind of rare now. Most (all?) are listed on the paper times guide you get when you enter the parks. I think there's a website which lists more. I ghaven't used one in ages so I don't know.