Sigil

Each portal needs a key, but it could be physical objects, a thought held in the traveler's mind, anything... Once activated by the correct key, how long does the portal remain open?

Depends upon the portal, but almost always long enough for a traveler to pass through. In many cases of a keyed portal, the portal will only be open for those bearing the key. Remember, a portal is not necessarily like a door - it can be effectively a "state" that authorizes certain entrants to pass on to other destinations. You and I might be tied together and leaping into the same portal sideways and it will only admit you because you bear the key.

'''So, if the key is a cold iron dagger, does the portal remain open only for the holder of said dagger as he passes through (which would mean each PC needs his own cold iron dagger)? Or would one cold iron dagger open the portal for a short time, allowing a party to pass through with only one physical key?'''

Depends upon the portal. If unspecified, you may rule as you choose. (But see the previous answer about passage being based upon a "state.")

'''In the case of a physical object serving as the key, does the object pass through the portal unharmed? Or is it consumed in passing through the portal?'''

Depends upon the portal. I'd adjudicate based on the thematics of the portal - are you planting a seed that blooms into a doorway? Consumed. Tracing a line with a silver dagger? Probably not, but who knows? Maybe the dagger melts and becomes the boundary of the portal.