Yes, the rules make clear that the Druid can only have one Druidstaff at a time, and that the Druid's spells will only affect his own Druidstaff. The rules don't say anything about others not being able to benefit from the +Spell Adder or spell multiplier effects, though, so I would allow others to use the staff for those benefits. The rule of one still applies though: the Druid might be able to give that staff away or loan it out, but he can't be in the business of arming an army.
On the issue of how long Attunement states, the rules don't make that clear as far as I can tell. Attunement is a static action, and seems to take at most a round. RMU might want to provide additional guidance in this respect by assigning and Action Point cost to it. I would suggest a full round (4 AP), since I expect it to take a fair amount of concentration.