by Dumon
@MaWaYes, you can collect in another territory on your next turn. If you meet the requirements there.
You cannot collect in a territory where you do not control a polis. The only exception being Achaia, as there is no polis in this territory. The first player to collect there will be able to do so each round.
...although it usually is not worth it, I came to realize...
@rcarabias
Yes and no.
The game is contructed so that you need to string your actions together to do so. As you righly mention, you need Prestige to collect in a territory. The only way to get prestige in decent amounts is to either besiege a city or to "purchase" one with the Proxenos. Then, you can once again move units, besiege another city, and so on...
And remember - your home territory does not cost prestige points, when you collect in it.