With the bonus from current masteries, MP pool from skills, loads of RE pots released from events, and Inspiration, MP recovery should never be an issue. That being said, I don't agree with the Karis set. As for Hebona set, the firebolt enchancement is minimal. Most likely, you're better off getting a Languhiris Chaser Circlet and get Fire Mastery reforge on that (easiest piece to make for dragon gears, btw). Usually I'm not an advocate of RKA, but in this case, I'd encourage it, due to MA's effectiveness with MS as well as ping.
Karis+Mana reduction with hebona is generally for folks who're dedicated to firebolting. As far as I see, they're not planning on hybridizing immediately or extremely soon so its their choice. Also, Fire mastery reforge is garbage compared to either a Lightning mastery reforge for Lightning rod, or a bolt mastery reforge(which at level 15 is essentially the same as a hebona set). And I'm not entirely sure of if 12 matk really does anything unless you intend to fully push towards magic, which is better for higher tier magic, but worse for firebolt, which is generally bread and butter aside from blaze and LR/Meteor and the odd hail.
Recently I've been liking that +10% reduction overall is better than the +20% ping from RKA, and that it curbs more mana from firebolt spam. Its all a matter of preference to be honest.
As for firebolt wand, you should really be going for R6 instead of S6, since the BFO will be more potent with R upgrades. Only reason you would S6 is if your gear is not based off of max damage. But then again, you're better off using Tribolt wand or Ego Firebolt Wand for damages. You can use Savage Fire Wand for blaze I guess, but I'd think Ice Wand is better for that due to IS + Blaze.
As for ego vs. regular wands... ego will always win out. There is one alternative that comes very close with ego, and that is Tribolt Wand. If you want to spend some time with Firebolt but not too much, that wand is your answer. Other wands are pretty much obsolete at this point if it weren't for blaze.
I believe they did state that, they might not have been fully clear, but it was stated nonetheless.
As for BFO vs. Vivace, it depends on your gear. If you have max damage gears, BFO will help you out a ton more.
Its generally not as simple as that. Its closer to if you have the vivace reforges rather than others. +40% speed from vivace gives a lot more than BFO in my experience. I, though, do not have the str and damage potential that a human would. So my opinion may be skewed. For the most part vivace hands a lot more control over things and juggling up to 3 monsters is extremely potent in multiaggro situations when aggro drop or lock isn't an option. If one doesn't go for the reforges BFO is default.
So what should your equipment look like? If you were to combine Mage/Final Hit/Gunner gear, this is what it would look like:
Headgear: Oblivion Dexterity Languhiris Chaser Circlet/Chinese Dragon Helmet/Random Wig. Reason for three? Game probably won't be nice enough for you to get all three on one hat. You'd want circlet for Magic related, CD helmet for Gunner (get Wotg duration 20) and FH CD 20 on wig.
Body: Sight/Long-Lasting Champion/Heroic RKA. I prefer sight over conceptual because of easiness of enchanting as well as more returns in general. The balance can help out a lot for guns. Champion and Heroic are pretty self explanatory, damages. I'd get Final Hit duration 20.
Shoes: Solo Viscount Languhiris Chaser Boots. You want the AS + 2 from viscount so that you can complete AS effect with Languhiris gloves. I'd get shooting rush damage 20 on this thing. You could opt in for Chinese Dragon boots, but I like the defensive stats Lang has to offer.
Gloves: Solo Camo/Backbreaking Lang gloves. Ideally backbreaking for enchant, but RNG can get you only so far. You want Combat Mastery damage 20 on it. MS reduction is essentially a waste when you get high MA.
That is if they go into hybridizing. Generally, going damage enchants far exceeds matk enchants regardless, its just a question of what they wish to do. They can go full mage route which hebona and the swapout wear, which can be karis, Languhiris chaser, or RKA. Millia's is an option for females as well, or hybridize without the hebona focus.