1. If the ally is not resisting, then all you need to do is know the weight of the carried ally and the strength of the carrying ally, then you just do a check to see how burdened the carrier is.
2. That's a very good on-the-fly GM ruling. You did good. The trick here is determining a DC for the catch. Some GMs might rule that an attack roll is needed on the throw too. But you did fine.
3. There are no rules about how far or fast fire spreads (at least not that I know of). Your approach is as reasonable as anything. This is a classic example of how a GM has to make rulings that fit their idea of how the world works. It's hard to call any such ruling "wrong". Your approach added a random factor the the decision, which is not a bad idea.
4. Tripping rules are in the core rulebook. Setting characters on fire is much more difficult to do. Dousing them with oil or grease first would help, then you could use guidelines from the book around oil used as a splash weapon as an example. Depending on how clever you want to be, you can make all sorts of unique rulings. You might also want to look up "dirty tricks" in the rulebook.
Sounds to me like you did a fine job. Welcome to the fraternity!
1. Carrying allies. In the campaign, someone ended up picking up the other person who attempted to run away from the battle, and dragging them back. I made it a simple reduce speed by 50% since they weren't resisting, but how would I normally handle this?
Calculate total weight of the ally and use the encumbrance tables. I'll wager you likely end up with the same result.
2. Throwing an item. Someone during combat threw another person a weapon, who was some distance away. How would I handle this normally? I just did a reflex DC 12 check to see if they caught it.
Again probably fine. I'd call for thrown weapon attack especially if it "was some distance away." Then a reflex save probably DC 10 to catch.
3. Setting fire. There's a pyro in the group who kept using her flint and steel to set things on fire (like straw mats, all piled about). I had her roll a d20 to see how far the fire spread (since there was a lot tile to tile with each other). How'd this be handled normally? In a forest?
I've never been real happy with any system for adjudicating fire spread I've seen. I just usually have rule it spreads slowly at first then accelerate as more squares go up, just like a real fire.
4. I plan to have goblins muck about more in the future, and have them try tripping people and setting them on fire, what nots. How would this work out?
Trip rules are in the book. See page 444 for rules on catching on fire. I'd say normal trip, pour pint of oil on them (see oil under equipment), then light.
2. Seems reasonable; I'd add to Tim's suggestion that the attack roll be against AC 10 since the target is not attempting to avoid it (Dex, armor, deflection, dodge, etc. bonuses really shouldn't apply).
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3. Setting fire. There's a pyro in the group who kept using her flint and steel to set things on fire (like straw mats, all piled about). I had her roll a d20 to see how far the fire spread (since there was a lot tile to tile with each other). How'd this be handled normally? In a forest?
A fire started in a highly flammable web spell spreads at 5 feet per round. For materials that are not quite so flimsy and tinder-dry, you could reduce it to a square per minute or per 10 minutes, make a saving throw to see whether each surrounding square catches before the burning area exhausts its fuel, or both.
1. Carrying allies. In the campaign, someone ended up picking up the other person who attempted to run away from the battle, and dragging them back. I made it a simple reduce speed by 50% since they weren't resisting, but how would I normally handle this?
It depends... I'd use the encumbrance rules, as other posters suggested if the team member act as "dead weight". If he was simply passivly opposing, I'd rule the 50% speed as you did.
2. Throwing an item. Someone during combat threw another person a weapon, who was some distance away. How would I handle this normally? I just did a reflex DC 12 check to see if they caught it.
I'd use the throwing splash weapon rules, where they say that you can target a SQUARE by making an attack roll against AC 5 (and, in a case of a miss, I'd use the splash rules to determine the square where the weapon land). Range increment equal to the range increment for a improvised thrown weapon (10ft IIRC).
After the attack roll, I'd use a simple DC5 Dexterity check. If succesfull, the player gets the weapon. If unsuccesfull, the weapon fall in his square.3. Setting fire. There's a pyro in the group who kept using her flint and steel to set things on fire (like straw mats, all piled about). I had her roll a d20 to see how far the fire spread (since there was a lot tile to tile with each other). How'd this be handled normally? In a forest?
Read the "web" spell... and multiply the time by a factor of 10 or more (depending on the particular environment), considering that the web threads are extremely flammable.
4. I plan to have goblins muck about more in the future, and have them try tripping people and setting them on fire, what nots. How would this work out?
I'd equip the goblin with alchemical or mundane oil or something, so they could make splash weapon attaks. After that use a normal CMB check to trip and have another goblin ready an action to make a (melee or ranged) touch attack with a torch.. :)
If the attack is succesfull, determine damage according to the particular substance being used (e.g. for mundane lamp oil, 1d3 fire for 2 rounds) or read the environmental rules on the PFSRD.What do you think?