The way I think about it is like this:
if your champion has a snare/root/disable/whatever, then Flashing in range and using it (pretty much) guarantees you can keep hitting them for a good while at least. Think Darius and his W-E combo, you can Flash in range of a champion, pull him to you and snare, then just keep hitting him.
if however your champion has no such disable, Flashing alone will get you one hit, maybe an autoattack too, then they run away. Here Ghost is more beneficial because you can keep chasing them. Shyvana is a very good example of this, although I like Ghost on Fiora also because her sprint ability is kind of short duration compared to the CD and she has nothing else.
You should however consider that Exhaust might be a better choice over Ghost for chasing/ganking purposes where Flash isn't "the right choice", because in addition to the snare, it also nerfs their damage output, so you can use it as a peel for your carries (or just straight dueling). I use Exhaust on both Nocturne and Shyvana for this purpose.
The argument above that Ghost is good at escaping... I don't know about that. You never really leave melee range if they snare you during it, whereas Flash opens a gap for you to let your snares run out and stops damage income cold. Ghost is also a one trick pony, whereas Flash can net you a huge tactical advantage by Flashing over walls that champions without Flash would have to otherwise slowly run around, or lets you escape turret damage instantly etc etc.
Try them all in my opinion, you'll get the hang of their strengths and weaknesses after some amount of games. I'll tell you that I miss Flash the most when I run Ghost or (more often) Exhaust, but I'd still never run a Flash Shyvana.
Yes Elise continues to take damage from debuffs applied to her during Rappel. She however does not take damage from Area Targeted effects during this time. It can therefore be used to 'dodge' many things, just not everything.
The wiki states, and I paraphrase;
'Untargetable' refers to champions in a state where targeted spells such as Rammus's Puncturing Taunt and LeBlanc's Sigil of Silence cannot be cast on the untargetable champion, and nontargeted spells such as Karthus's Requiemwill have no effect. Additionally, they cannot be targeted by auto attacks.
It also lists the description for Elise's Rappel skill as;
Rappel is a point targeted ability with two effects. If an enemy unit is targeted, Elise and her spiderlings will become untargetable for about 1 second and will move to the target's location. If Rappel is cast on the ground, Elise and her spiderlings climb into the air and become untargetable for up to 2 seconds. While in the air, Elise is granted vision of a large radius around herself, and may target an enemy unit within this radius with Rappel to descend upon them, moving to their location. If the 2 second duration expires, Elise will descend at her original position.
Nothing here mentions anything about single target debuffs that have already been applied, ongoing effects and the like, including but not limited to leashes such as Fiddlsticks' or Morgana's, or ongoing damage over time debuffs such as Malzahar's Visions or Summoner Ignite. Therefore it should be assumed they perform normally once applied.
sources:
http://leagueoflegends.wikia.com/wiki/Elise/Ability_Details
http://leagueoflegends.wikia.com/wiki/Untargetable
Best Answer
Elise lands directly on her target. But if the target moves she will still land where it stood before. See the Lol Wiki description