No, multiple instances of the burning ground damage from Fire Trap will NOT stack.
Only different sources of burning damage can stack. For example, an Ignite debuff from a spell's critical hit and the Fire Trap ground burn will stack.
When 2 of the same burning sources are present the highest damage source will take effect. Multiple effects can still apply, like 2 Ignites on one mob, but only the highest damage one will actually deal damage.
Once the highest damage effect ends, if another instance of that effect was applied and still has duration left, it will then do what damage it has left. This goes for Righteous Fire, Ignite, and Fire Trap's ground burn effect. Searing Bond, a recently added skill, is an exception and the beams can stack with itself.
This is why you should try to spread out Fire traps a little bit whenever possible.
Posted by Mark_GGG, PoE developer and creator of the games skills and their mechanics.
...Ignite, RF, ground fire and now Searing Bond are all separate
sources of burning damage, and all stack. Ignite, RF and ground fire
do not stack with themselves (only the highest of each takes effect at
a time), but do with each other.
Searing bond beams stack.
As of Patch 1.0.5 Searing Bond Beams no longer stack.
No, the quality of a weapon only affect the physical damage part of that weapon (local). The attribute you are describing (skill gems on this item are supported by lvl 30 echo) is the implicit mod of Pledge of Hands (unique). Some items may have implicit mods, but cannot be improved in any way.
As a side note, you can change or add (to those items that don't have) an implicit mod with 'Vaal Orbs', but are very dangerous to use because they can change your current implicit mod (if there is one, so only use it on items with non-interesting implicit), change one/multiple of your socket colors to white, or reroll your item and change it completely. That mean that, if used with uniques, a Vaal Orb can break your item and convert it into a rare item (yellow). Don't use it with your Pledge ;).
Best Answer
I don't think so.
To my knowledge you cannot alter gem tags. Your setup will add cold damages to every hits of the main skill, but will not change the attack skill to a cold skill.
In case you don't know, there are very detailed informations about every equipped skills in the offense section of your character screen. There you can take a look to the
% crit multiplieroftornado shotan see if it is affected directly.(If you can test it, please tell us the results!)