I am unable to find an answer to this.
If a caster has an antimagicfield cast on themselves. Can they cast a spell that has effects outside of the field.
For example, could the caster use holy smite targeting only targets outside of the field. It is not being "cast into", "brought into", or "used within".
An antimagic field suppresses any spell or magical effect used within, brought into, or cast into the area, but does not dispel it. Time spent within an antimagic field counts against the suppressed spell’s duration.
Casting is using within, so nope.
, , , Unless you are a 10th level Blackfire Adept, but then the catch is that if you succeed, you destroy the Antimagic Field (on the other hand, you can potentially although not easily succeed in a natural dead magic zone without destroying it, and on the third hand, if it's somebody else's Antimagic Field, you probably want to destroy it). Note that you can dismiss your own Antimagic Field, although this requires a Standard Action, so if you want to disable your opponents' magic, and then suddenly spring a spell on them, you can do this if you can Quicken the spell that you cast right after dismissing it (or if you have a spell that is already Swift Action).
Backfire Adept doesn't progress the Summoner's Summon Monster SLA (nor does it progress the Eidolon).
If you just want Summoner spellcasting, sure, but you're probably better off with a Conjurer Wizard or a Sorcerer.
Doesn't really matter, since the Master Summoner still needs the Summon Monster SLA, which stops progressing once you enter a prestige class. Assuming you enter Blackfire Adept as soon as possible, from level 5 to 15 you won't be able to use anything better than Summon Monster III. At level 19-20, you'll have SM5.
...
Normal Summons aren't restricted to just one group at a time. Only the Summon Monster SLA of Summoners is.
(Maybe PFS restricts it, but Master Summoner isn't allowed for PFS.)
And if you want standard action summons... Again, that's just the SLA. If a Summoner casts Summon Monster as a spell, they need one full round, as other classes.
And even if you have some houserule that extends that limit to all summon spells...
"If the summoner’s eidolon is not summoned, the number of creatures that can be summoned with this ability is only limited by its uses per day."
Master Summoner only allows multiple summons with the SLA (because other summons were never restricted in the first place).
The only advantages (chained) Summoners have are their Eidolon, their ability to spam high-level Summon Monster SLAs, and that they get some high level spells as lower level spells.
Two of those are rendered useless by nearly all prestige classes (Evangelist being the one exception I know of), and the last one is primarily an issue for wand and scroll pricing.
Basically, anything a Summoner (including archetypes) Blackfire Adept can do, a Conjurer Blackfire Adept can do better.
Depends.
Ninth-level casting with Blackfire Adept on one side, Master Summoner with its SLA on the other? Yeah, that would be pretty good.
Reduced (sixth-level) spellcasting on the Blackfire Adept side (or just Summoner, but the Prestige levels alone are Gestalt, or something)? Meh. Several of its abilities key of the levels of sacrificed spells. If your spell level progression is delayed and cut short at 6th spell level, then you get reduced use out of it.