Question: Flame totem + support gems

I have a few questions on flame totems and how they interact with other support gems. I've done some research on this, but haven't found any answers that are recent enough or that answer my questions to satisfaction. I hope someone can help.
Regarding the faster casting support gem, does that increase the rate at which flame totem shoots its flames? There does seem to be a DPS increase, according to the tooltip description... but is that just figuring in the reduced summoning time for the totem, or is there actually a greater output of projectiles?
Second is multiple projectiles. Obviously this works, but does it have a shotgunning effect? In other words, does more projectiles = more damage against a single enemy? Or is it like split arrow, where each target can only be damaged by a single projectile from the group?
Oh... also, what sort of effect does spell echo have?
Thanks!

FT definitely shotguns. Can't say anything about cast speed though (my opinion is its just summoning speed though).

faster cast affects both your speed of summoning totems and the totem casting speed. You should definitely aim to use GMP but feel free to test kill speed with/without it (the cast remains in a narrow streak for each stream). Spell echo does nothing.

For a 4-link I recommend flame totem - fire pen - faster casting - GMP
For 5th link add either added chaos damage or faster projectiles.

As an aside, there are some bugs with sheet dps on totems so do not trust it too much. For example the signature passive Totemic Zeal will increase the sheet dps substantially even though it doesn't affect the totem's casting speed (confirmed by devs). I am in two minds as to whether totemic zeal is worth the investment although putting down totems faster and having them starting to shoot sooner is going to increase their survivability.

That's very helpful. Thanks!

knockback is pretty awesome with flame totem ;)