When a target is hit with multiple attacks, through the use of Full Auto or Lightning Attack for example, and the force field absorbs one or more hits, do all of the attacks resolve before the flash grenade or teleport effect take place? Or if someone gets blasted by a storm weapon do they just end up teleporting away before getting shot to bits by multiple unblocked hits?

With the conversion field, I'd say that the hits from autofire (ie, same to-hit roll) don't care which hit is the one that got blocked by the field, the first or the last.

With the teleport field, I'd say resolve in order, that is, if it's the third of five hits (you had an awesome roll when testing BS) that triggers the teleport field, you roll damage for the first two hits and ignore hits four and five.

I don't remember is the BC Lightning attack multiple WS rolls or one single roll? If multiple rolls, the rolls that would come after the field trigger get the penalty (if conversion field) or are wasted (if teleport field). If a single roll, it's the same as using a gun for the teleport field (hits before triggering are resolved as normal, but subsequent hits are ignored/wasted), but single WS roll on Conversion field? I'd apply hits prior to the field trigger as normal, and then recalculate using the same roll, but applying the penalty to see if subsequent hits still happen.

With the Storm quality ... I'd not check the field against the Storm-generated hits. Instead, the field would be checked as a regular weapon, and then the hits prior to the field being triggered would be counted twice for damage purposes as per Storm.

This does make the Storm quality potentially very good against field defenses.

I'd say it has a chance at avoiding the following attacks. Remember FA allows you to hit within a distance so they may not displace out of danger. As for Melee, yes they avoid the follow on attacks unless they somehow manage to teleport still melee.

The conversion field while logically would affect follow on attacks, the roll has already been made which is what would get modified.