1) Code not tested, tweak as necessary.
Post Level 10000
Code:
~ Add +1d6 fire damage to any weapon which is not already flaming
~ This iterates through all picks we have which have attack and damage fields, looking for those with either the "equipped in main hand" or "equipped in off hand" tags AND not the flaming weapon ability
foreach pick in hero from AttDam where "(Hero.MainHand | Hero.OffHand) & !Ability.iFlaming"
~ We have found one! Apply extra damage text and mark it as flaming so any further abilites don't stack more damage.
#extradamage[eachpick," plus 1d6 fire",field[thingname].text]
perform eachpick.assign[Ability.iFlaming]
nexteach
2) The simplest way would just be to add the tags to track your rounds/day to the armor and have the item itself show on the specials tab with an appropriate summary.
Alternately, you could do it sort of like the Thanatotic plate (from book of the damned) does with its situational spell resistance pick. Create a simple ability which calculates its charges based on your hit dice and bootstrap it to your armor with a bootstrap condition for being equipped.
3) Not really an appropriate place to put a situational, really. The Damage pick is for damage you inflict, not damage you take. I think this would just have to be included in the summary of whatever you do for item 2 above. If you really think it needs to be called out you could even make it a separate ability shown by itself when the armor is equipped.