How many times can Proxima Cenatauri Scholars use its owner benefit?
The answer is Option A: you may make one placement or removal (not both) per turn. Your suggestion of spending 6 fuel to score an agenda is quite creative, and almost certainly not anticipated by the designers &ndash; there's normally no benefit at all for moving a single field generator multiple times (except, I suppose, to destroy the Relic Ship with the Isolation Field).

I do not have any specific rules text to back me up, but the Alien Frontiers rules are intended to be as straightforward as possible and allow useful, but not crazy, interactions. There are a handful of weird combinations that were not prohibited by the rules, but were disallowed in later errata. Here's a few examples:


Ain't no rule that says you can't use the Plasma Cannon's discard power to destroy a player's fourth ship while they have one ship sitting on the Terraforming Station (and thus they'll be down to two ships on their turn).
Ain't no rule that says the ships on the Raider's Outpost matter if you remove one with a Plasma Cannon.
Ain't no rule that says you can't discard the Plasma Cannon to destroy a player's third ship when they also own the Relic Ship. (Have you noticed that the Plasma Cannon has the most weird interactions?)


The point is, you get full points for creativity, but you're stretching the spirit of the rules pretty badly and that's exactly the kind of thing that gets errata'd in Alien Frontiers. The creators run an Errata thread over on BoardGameGeek, if you'd like to ask them directly: http://boardgamegeek.com/thread/572710/rule-book-errata/page/2

(My logical fallacy is: Appeal To Authority. I've played Alien Frontiers with Randall Bart, the designer of the Alien Frontiers: Outer Belt expansion and early playtester of Alien Frontiers.)