Throw the letter into the room before the guards take your stuff, then pick it up afterwards.
You can get another axe to give to the king;Lost Items - guide and directory of inventory files
When your equipment is removed, you no longer have the vitality/mana/constitution/intelligence bonuses, so your maximum health and mana drop. When you get them back, the maximum return to the previous values, but not the current values.
You can toss a teleporter stone past the guards to avoid them.