So far in the game, I haven't found dragons a serious threat to my own safety - the most I've encountered are 2 frost dragons at the same time (yes I know there can be more). As a Bretonese Alchemist, I'm always loaded down with health potions and I can become mostly impervious to magic if I want to. However, what I really find upsetting is when NPC's get killed by them before I manage to kill the dragon with arrows (or a one-hand if it lands). Every time it happens, I feel as though I've failed the people. Not to mention the possibility of having quests fail because the quest giver dies. This is especially frustrating when the dragon refuses to land, which means it takes me longer to kill. I've learnt to concoct potions for almost any situation, but what I still don't understand is how dragons respond to potions and poisons. I've just learned from reading the Wiki that they're immune from paralysis.

Are they immune to other poisons?
Do they respond to a poison of "slow"?
Is it better to use a poison that damages their health, stamina, or magic?
Do dragons use stamina at all, and if so, when?

At the moment, the only potion I know is guarantee effective is a potion of True Shot, since that increases my archery damage.

Has any alchemists out there figured out the best strategy to take down dragons as quickly as possible? I want to minimize their damage as much as possible.

Dont be a [censored] Alchemist.
Become a Forsworn and ask 20 Septims a Lapdance.

All dragons are immune to paralyze.
Frost dragons resist frost and fire dragons resist fire.
Those are the only resist and imunities that I know of.

I know for sure that health poisons and lingering health poison work against all dragons.

I'm not sure about poison of slow but a fire dragon does not resist the slowing effect of a frost spell,so I would assume a slow poison does work on fire dragons at least.

I've always found it best to use lingering damage health agianst dragons.
I also like to unload all those frostbite spider poisons I find on dragons.

Yes fortify marksmen potions work great.

A tip.
If you put a few perks and get some levels in two-handed,you can make a fortify two-handed/resistfire/regenerate stamina potion that can totally destroy most draons in seconds.
Once you get them to land,pop a potion and start power attacking with a two-handed weapon endlessly,lots of fun.
Alchemy is one of the most powerfull skills in this game.You don't know what your missing.

'Bretonese'?

and the least useful post award goes to you! huzzah!
alchemy is freaking uber, as you already know being an alchemist. slowing poisons do work on dragons, but i've only found it considerably noticeable when they are flying.
dont fret about stamina/magicka poisons with them. focus on killing them, you can make a poison of slow/damage health using deathbell/salt/any other ingredient with damage health. or deathbell/river betty.
not sure if frost's slow effect stacks with the actual slow effect or not but it's worth a try.

Alchemy perked out is nuts and a supped up lingering damage + slow potion that stacks twice because of concentrate poison will wreak a dragon. My first character was a sneaky thief who only used daggers and had no weapon skills at all. Of course I would destroy anything in the game by sneak attacking it but that crap almost never works on dragons. I found that after I focused on alchemy high level dragons became a joke and I would always walk around with several potions to be used only on dragons. Alchemy is very viable vs dragons and very useless vs undead and automatons. I only used alchemy as a craft skill and nothing else as well.

I disagree with the useless vs undead and automatons part here.
Fortify potions are awesome.
A fortify marksmen potion with no perks in alchemy and an alchemy level of 20 can increase your archery damage by 20%.
Thats not just your bow but your arrow damage as well.
20% is a free overdraw perk without taking any perks.

Now start to perk alchemy and overdraw and see how far alchemy agianst the undead can take you.

Poisons are awesome but they are only half of what alchemy can do.