Armed to the Teeth is achieved by equipping all inventory slots with level 25 or higher items. Prepared for Battle is similarly achieved using level 60 items. Will level reduction modifiers prevent me from getting these achievements?
The game uses the "true" item level to determine several things, such as item type, salvage materials, and most importantly, what affixes can be used. The Reduced Level Requirements is just another affix that is applied against the item. I specifically tested this affix when checking for salvaging. Based on this logic, Reduced Level Requirement affixes do not affect the true item level.
Incidentally, searching for only level 60 items on the auction house will still bring up items with this affix.
No, because the game uses the internally stored item level to check if you should be awarded the achievement.