1. What happens to your turn mode and speed when you tractor it? It is moving speed 8, but there isn't any information about its relative 'mass'. I would assume it's like tractoring a ship with twice your movement cost, you slow down by two baseline speeds and use that turn mode.
2. Since the amoeba moves randomly, if you are at range 1 and the die roll forces it to move to range 2, is your ship dragged along? Is the tractor beam broken? Does the amoeba not move? Do you roll again?
This scenario was tough in a Fed NCL since there are only 4 lab and for some reason, every time I would roll for damage (quite often since you need to get close enough to effectively use you labs and some damage will leak through your shields), I would roll a 3 or 4 which damaged one of my lab boxes, reducing my overall lab points gained for that turn. It was scary when I got to turn 13 and had to roll for how to kill the amoeba. I was dreading getting the result of gathering more information and then rolling again. If you're unlucky enough, you could conceivably keep rolling that result until the scenario time limit hits. A very disappointing way to lose a solitaire scenario.
With 10 lab and 4 special sensors that's effectively 14 lab boxes, plus two probe launchers (up to 180 lab points per turn!!). You should be rolling to kill the thing in 3 turns if you are aggressive.
