1) Yes.
2) Yes, and it's not double cost.
3) Since there's no minimum distance listed, yes, but if I were your GM, I would have you make a DC 15 Fly check to hover.
Flame Jet has no text saying you can hover, so I'd say no. It's pretty clear on what you can do with it.
It wouldn't be hovering, but you could probably ease your descent a bit by continually blasting upward each round, though the Environmental Rules say you can't cast a spell (which probably extends to SLAs like Flame Jet) that isn't an Immediate Action unless the fall is more than 500 feet and you make a concentration check. I'm not sure how falling speed works, but if it is 500ft. per round, then you'd probably only take a little over 30ft. of fall damage.
What I want to know about Flame Jet/Greater Flame Jet is if they're worth the 2 Wild Talents when you can just get Ride the Blast for one Talent later on (my group is not PFS and the game I'm going to be playing my mono-element Pyrokineticist in is starting at 7th level).
Flame Blast (or Self Telekinesis) aren't that useful in combat; they're mostly for getting across chasms and on top of buildings and things like that. The greater versions though are worth it for the "you are always flying" aspect, but it's worth considering whether you're going to expand into air since the air "you are always flying" talent works better and has a less redundant prerequisite (take the "you are constantly under the effect of feather fall" one.)
Greater Flame Jet/Self TK are 5th level talents, so you'd get them at level 10, but if your second element is Air (and you snag Air's Cushion with either your level 8 utility or (a better option) a "extra wild talent" feat taken at 7 or 9), then the better flying comes online at the same level.
While flame jet and greater flame jet (and similar talents like self-telekinesis) are limited to straight lines per action for traveling purposes, it does have one advantage over Wings of Air: the speeds don't have the restrictions of armor or encumbrance that the fly spell Wings of Air imitates has.
Since Kineticists are dependent on two attributes and one of them is dexterity and only get proficiency in light armor, you're probably not going to spend a lot of time in armor that slows you down and you're not going to be carrying a lot (especially the telekineticist). If you're building for something in heavier armor, or you want to carry a lot of stuff, that's a good thing to be aware of though.
I like flame jetting around carrying allies who don't have flying abilities. Whether it's going up way high cliffs, carting an ally with appropriate weaponry to the flying shooting BBEG with the hardness/DR/energy immunity that makes my blasts annoying ineffective, or just being kinda Mighty Mouse about it.
Yeah, of course Wings of Air is better, but I'm taking Fire again as my Expanded Element at 7th.
The thing is that you can get great mobility with Ride the Blast even with out-of-combat uses, as it's basically like an improved version of the basic Flame Jet. I'm also wanting to take Spark of Life at 10th, so Greater Flame Jet would wait until 12th, which is the same level as Ride the Blast becomes available.
I'm thinking of maybe going VMC Oracle for Flame Mystery (Gaze of Flames in particular is much more useful than the Firesight Wild Talent; the VMC comes with a free fire extinguisher via at-will Create Water, too) and Powerless Prophecy Curse (Staggered first round? Who cares? I launch fiery death with Standard anyway!), so I'm not going to be able to spend a ton of Extra Wild Talent feats (Feats will likely be PBS, Precise Shot, Elemental Focus[Fire], and maybe 2 Extra Wild Talents). If I don't VMC, then I'd need to use some of the feats on Extra Wild Talent to pick up the things that I'd get the equivalent of through the Mystery, like Firesight and maybe Heat Adaptation. I think you can see why I'm concerned over using up 2 Wild Talents to get Greater Flame Jet, especially when I can think of many uses for Ride the Blast and getting both would be a little redundant.
Sure, I wouldn't be able to stand in the air and break the game, but that's really not what I'm out to do and we'll be getting 2 new players into the game with this campaign, so it shouldn't be incredibly difficult (part of why I decided to try out Kineticist and Pyro in particular).
I like flame jetting around carrying allies who don't have flying abilities. Whether it's going up way high cliffs, carting an ally with appropriate weaponry to the flying shooting BBEG with the hardness/DR/energy immunity that makes my blasts annoying ineffective, or just being kinda Mighty Mouse about it.
We're going to have a Bard and a Druid in our party, probably an Arcane full-caster of some sort, and a Slayer. Flying shouldn't be much of an issue later on with those around, and I don't think my GM would be mean enough to make TOO many things completely immune to fire.
Besides, my 1d6 Kuru racial bite attack is TOTALLY enough to deal with fire-immune enemies, right? I mean, not only can it deal damage on the rare occasion I actually manage roll a hit with it, but I get ONE WHOLE TEMP HP when I bite something that has blood!
This is getting into Advice territory, but I think if you're going fire/fire, then taking the flame jet utilities is reasonable since fire doesn't have all that many amazing utility talents to begin with (of the five basic elements, fire probably has the weakest utility). It seems to me that of the level 1-5 fire utilities there are 7 in fire that are worth taking including the 2 flying abilities. You'll get 5 utility talents by level 10 (when you could take greater fire jet).
So definitely take Fire's Fury and Searing Flame at levels 2 and 4, and if you're going VMC Oracle for Gaze of Flames, the only good choices at levels 6 and 8 are Flame Jet and Smokestorm, so the choice at level 10 is between greater flame jet and fire shield, which form a stark contrast depending on your willingness to get hit.
Elemental Whispers isn't bad at 6 or 8 for Alertness feat and ability to manifest a little creature via concentration. Elemental Grip wouldn't be a bad choice, either. Neither compare to Smokestorm, of course, but if I'm picking up Ride the Blast at 12 then Flame Jet isn't too important unless you're expecting to get into a lot of specific troubles.
Getting a bit closer to the topic, Flame Jet just seems a little underwhelming by itself, with Greater Flame Jet being what really makes it. It's too dangerous to use vertically by itself for anything more than subverting simple Climb checks, so unless you're crossing a gap it seems mostly unneeded.