Buzz Lightyear is the only disconnected attraction FP. The shows (WoC, F!, Frozen at Fantasy Faire) and character meet & greet (A&E) are disconnected from their respective park's FP system. So, yes, in theory, you can get a HM FP and then go directly and get a F! FP (or Buzz Lightyear). The two parks remain disconnected as well, meaning getting a FP in DCA doesn't impact your ability to get a FP in Disneyland.
You can get the WoC FP at the FP machines near Grizzly River Run. The F! FPs are distributed along Big Thunder Trail about half way between the Mark Twain dock and Big Thunder Ranch.
Assuming that Haunted Mansion has Fastpasses going, yes. Also, you can get another Fastpass either when your window opens for the one you're already holding, or two hours after you pulled it, whichever comes first.