The sensor array eventually was destroyed with multiple hits over time, but the GM claimed it could be repaired during the fight by the opposing crew. Our group argued that it would have taken external repair (ie, a spacewalk) to fix; something we think anyone would not choose to do in the middle of a battle. How would your campaign determine repair matters?
Depends. Two things to bear in mind are that repairs doesn't necessarily mean a spacewalk because it's not necessarily a replacement or welding job; the fact that the main sensors are wrecked doesn't meant that it's not possible to reroute systems electronically and get some sort of capability back. Equally, many ships will carry AI or remote operations repair drones, who can go out and look at the wreck of the sensor arrays. Equally, the damage need not necessarily be entirely to the protruding bits; it could be that the signal processors have been hammered by a shot that breached the hull.
Equally, fuel damage doesn't necessarily mean 'blown off the ship' - it could just as easily be the web of piping and pumps damaged; so the fuel's still physically there but you can't get to it. Which is fixable. Ish.
The Mechanic skill check for repairs is fine. Bear in mind that these only last so long; and break down again (permenantly) afterwards. Also that a check restores a certain number of hits, which may not help. For example, a sensor array which is destroyed (3 hits) and repaired by 1 hit (2 hits) is still counted as disabled, so it doesn't help you unless you roll a very good effect and push it back up by 2 or more hits.
The other issue was that the enemy ships fuel tank was eventually destroyed. What effect besides loss of propulsion would occur? Could the ship spin or turn facing? How about power to laser turrets or missle racks? Could the ship even self destruct if there is no fuel to detonate?
In order:
1) Spinal weapons or weapons in fixed mounts (rather than turrets) should probably become useless as you need to align the ship to fire them.
2) Assuming the ship draws J-Drive and P-Plant fuel from a common pool, then loss of all fuel means that eventually it will lose power. It'll take a while for that to happen, though - you've still got the fuel within the reactor system itself, and that will last a while; if a plant only burns through a few dTons in a timescale of weeks, it'll quite happily keep going for a few hours on the leftovers elsewhere to the main tanks. Also, missile racks are generally considered to not draw much in the way of power - that's why they're not listed as "energy using weapons" in High Guard (where it lists what a ship can and can't do when operating off emergency batteries)
3) If the p-plant is still functional, then it could still self destruct. Wait long enough for it to burn through the remaining fuel and you wouldn't be able to set off the plant, but certainly within a short timescale you could. Also, a missile equipped ship could detonate its magazines, and some ships might carry specific scuttling charges.
enemy crew decided to scuttle rather than surrender.
Interesting. That suggests some serious motivation - either they were certain you were going to kill them anyway, or they didn't dare let anyone on board the ship for some reason. I smell conspiracy...
(as a footnote, if the crew were prepared to suicide, then they'd definitely be prepared to attempt a combat EVA spacewalk)