Since not much is know about merpeople these are my thoughts:
I would assume that they would use found undersea items to craft weapons and armor, or occasionally, things found in shipwrecks. Items like sharpened coral or natural rock would work well for spear points and blades(of any length), and could be used to reinforce armor, but could get heavy and unwieldy if used for an entire suit of armor. I would imagine a more "leather" armor approach using woven seaweed (or other tough underwater plants, interwoven with strategically placed, shaped coral, rock or shells to protect vital organs). Possibly consider a "new" undiscovered plant grown by the mer-folk specifically for the armorcraft.
I don't imagine poison would be a good option, because once extracted from its source (animal, plant or synthetic) it would be nearly impossible to apply to any kind of weapon without the water washing it off or affecting an entire area, thereby polluting all of the environment in the surrounding area. There is no way to isolate a specific area for poison dispersal, so either an anti-toxin would be needed or a different approach. This would also have an effect on the surrounding flora and fauna of the sea, and I imagine the merpeople to be more eco-conscious than their land-dwelling counterparts and would decide on a better, more effective method.
Typically plant and animal based toxins need to be ingested or delivered directly into the bloodstream to be effective. Consider giving the merpeople some form of natural defense mechanism that utilizes toxins by touch or under their fingernails, used as a last resort, scratching the skin could administer the toxin or some other method. Maybe even a dissolving bullet/projectile, or false tip on a blade, that contains the toxin and is released once it enters an enemy body. Or contains a large enough dose to kill/paralyze an enemy, but small enough that if it dissolves on the ocean/sea floor, it wouldn't be harmful.
Any kind of traditional "gun" would be difficult to build for underwater use. Combustion is a key component of using a FIREarm and would not hold up to long-term use well. However, a more crossbow approach for projectile weapons could be considered. Using a somewhat heavy, sharpened object would likely be effective, but any projectile would not be very useful underwater unless a very great force could be used to propel it or if used for mid-range combat. Water, obviously, is very dense and creates much resistance when trying to move quickly, whether defensively or offensively. Spears would be the best bet for long-range attacks, or maybe some kind of spear-launcher, for added range.
As for mounts, I think that sharks and dolphins would be a good bet, but really, merpeople are equipped with the same mode of transport...are they really faster? Dolphins would be a more intuitive choice since they are more intelligent and would respond better to the interactions. Sharks, obviously, would be more lethal and would probably be used by more practiced, disciplined hands.
I hope these thoughts make sense, and I hope that you can create well-defined, believable world! Good Luck!