Right, got a reply from Sam Stewart. Summarised conclusions below:
1) You can use Brawl weapons with two-weapon fighting.
2) Brawl is intentionally open to interpretation, but yes you can use it with the two-weapon fighting rules as a kind of "flurry of blows". Sam does point out the increased chance of failure doing this however.
3) Therefore you can also use two-weapon fighting for a knife and fist/foot attack.