Bogardan Hellkite
Does my opponent have a chance to respond to the 1 point of damage by casting Brute Force on his creature after damage has been distributed?
Or would he have to cast Brute Force on his creature in response to the Hellkite trigger, and then I could assign 4 points to it instead?
See Section
409 410 of the Comprehensive Rules (too long to copy/paste here in its entirety). In summary, when you play a spell or ability (in this case, an ability), you do the following in order:
410.4. When a triggered ability goes on the stack, the controller of the ability makes any choices that would be required while playing an activated ability, following the same procedure (see rule 409, “Playing Spells and Activated Abilities”). If no legal choice can be made (or if a rule or a continuous effect otherwise makes the ability illegal), the ability is simply removed from the stack.The pertinent parts of 409:
1) Choose a mode, if applicable.
2) Choose the number of targets, then the targets themselves, if applicable.
3) If the spell or ability affects several targets in different ways, the player announces how it will affect each target. If the spell or ability requires the player to divide or distribute an effect (such as damage or counters) among one or more targets, or any number of untargeted objects or players, the player announces the division. Each of these targets, objects, or players must receive at least one of whatever is being divided.
EDIT: My mistake, Rule 409 only applies to spells and activated abilities. You want rule 410. The end effect is the same, but all the stuff about paying costs is extraneous.
Once all of this is complete, then the spell or ability is considered played and put onto the stack. In this particular case, you must already have chosen the targets for and distributed the damage for the triggered ability by the time the ability is on the stack, and your opponent can respond to save his 1/1 with Brute Force.
Ok, say I attack with a creature. My opponent activates his Mishra's Factory. Is there a point of time during all of this where I can cast Swords to Plowshares targeting Mishra's Factory before it is declared as a blocker?
Yes. At the end of the declare attackers step, starting with the active player, each player gains priority to play spells or abilities. This is the point at which your opponent will most likely activate Mishra's Factory. Once that ability resolves, each player will again receive priority to play spells or abilities starting with the active player; at this point, you can cast Swords to Plowshares on the animated Mishra's Factory before the declare blockers step.