+6.

The catch cost is applied once to the sum total of the power cost. If you take Physical Immunity as well as the Tougness and Recovery, you can take a stacked catch (one which applies only to the Physical Immunity, but which adds to the rebate from the first catch.)

The example in the book gives a stacked catch with a 5 point rebate, so using that example and your example above:

Supernatural Toughness + Supernatural Recovery = 8
Physical Immunity = 8
Total = 16

Catch for Toughness and Recovery = 2
Catch for Immunity = 5
Total = 7

16 - 9 = 9

As I read it:

1. Fate Point to GM
2. Fate Point to NPC
3. Fate Point to NPC
4. Fate Point to NPC - consequences are aspects just like any other, and the same rules apply
5. Fate Point to PC - self compelling a consequence is still a compel

Page 106 says (under the heading of 'Invoking other aspects') that "if you’re invoking an aspect on another PC or on a NPC to gain an advantage over them, that character will receive the fate point you spent". NPC compels work exactly like PC compels as regards where the fate point goes. The only time a Fate Point won't go to an NPC when you use one of their aspects against them is if you're 'tagging' - which involves no fate point spend.

The simplest thing to do might be to create it as an enchanted item (a ring or something) that has multiple uses. Not exactly what the player was looking for, but there's nothing to stop you tweaking it for flavour.

Alternatively maybe she's seen something of the future and there's a thing that she needs him specifically to do. Maybe he wasn't picked at age 16, maybe she's been watching him since birth, waiting for him to grow old enough to hold the power. Faeries being faeries it may be that the thing she needs him to do is something perfectly innocuous, it just has to be him specifically that does it, or it could be that she's using him to keep the power from being reassigned by her mother (maybe there's a special someone that the Queen want's to name asKnight, but the Lady doesn't like). At that point you've got the Knight being assigned really dangerous tasks by the Queen in an attempt to get him killed (because she can't be seen to do it herself, after all , he seems loyal to the court), and the Lady trying to keep him out of harms way by putting him in more low threat diplomatic situations (which may inevitably turn out to be more complicated than they appear).

Yes there is a little bit of vagueness in the rules. Page 116 defines a Declaration as taking no time at all. But elsewhere it's described as a kind of assessment, and an assessment is defined as a simple action, a category that also includes things like climbing walls etc. I guess you can interpret it either way.

2: Yes, decelerations should cost a fate point every time.

No, they either require a Fate Point, or a successful skill roll. The example on page 116 bears this out, and the description of declarations on page 20 states that they can normally be done with a skill roll, but spending a fate point makes it certain and there's no need to make a roll.

And from page 196:

To make a declaration, state the aspect you wish to create or take advantage of. The GM assigns an appropriate difficulty, and you roll the appropriate skill. If you succeed, the fact is true and the aspect is immediately assigned to the target so that you can use it just as if you’d succeeded on an assessment roll.

A sticky aspect lasts until the person it is applied to makes a maneuver roll to remove it or until the end of a conflict or scene. The type of roll to get rid of an aspect depends on the aspect itself. 'Sloppy Fighting Technique' might just require a discipline roll to 'get back in the game', or it might stick with the thug through the whole fight.

It is a free action, but the GM has the power to veto it if the players start taking the mickey - remember that it's a tool to make the GM's job easier. If it starts making it harder then you need to talk to your players about appropriate uses of declarations. The use of a roll for declarations isn't actually an optional rule, except in the sense that when making a declaration you have the option to make a roll or spend a fate point.

And remember, if they fail a roll they may not realise it until too late.

"Hey, that thug has a sloppy fighting style! Leave him to me!"

"You know, I'm beginning to think that might be Drunken Monkey Kung Fu... I've never seen someone beaten into unconsciousness with their own fist before. Still, it sure did look like a sloppy fighting style from a distance. Maybe we should call an ambulance..."

Apparently you posted while I was editing my previous response. RAW I understand. What's ROI?

Why would the GM accept?

"I'll compel his x aspect!"

"He's going to buy that off."

"I'm going to escalate"

"It's a compellable circumstance, but it's not that compellable!. No deal."

The box about escalation sepcifically puts it in the hands of the GM and states when a player can up the ante, and it's only on GM initiated compels. Aside from anything else the escalation rule should only be used in a defining moment for a character. It's not really the player's place to dictate that to the GM for an NPC who they don't know that well - the GM has a list of all of the PC's aspects and is in a better position to judge when their high concept is in play and when they are facing a real crunch time on that high concept.