For the axe: Good stuff, this is one thing I learned (and the half-sword combat).
On the arbalest being 0 DEF, my question was more: why does the flail provide a penalty (-1) to DEF, while the arbalest provides none? I can't see the flail as being more of a hindrance than the arbalest in defending against attacks. I would simply put the flail at 0 DEF. I.e. you don't use it, but it's not hindering you, is it? To balance it, I would look to reducing its damage die to d8 for example, making it a good weapon since not only does it reduce DR but also it's great vs a shield wielder.
By the way, I would certainly make the arbalest the only weapon with a 3 or even 4 DR reduction. As far as I understand, you can't do much against a loaded arbalest, even with heavy armor. Mechanics-wise, this would further balance it with regards to the bow that load more quickly.
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On the matter of initiative and reach weapons:
You haven't addressed my suggested rule:One thing that the rules do not account for is that if I am closed in on you with a dagger and you have a polearm, you lose any advantage that weapon has. I do not really want to get crazy complicated with things like that, but adding in factors like reach might lead to questions like this. I am not sure how to implement this in a system without miniatures (and I don’t want to use miniatures)
When it's the melee weapon combatants' turn, on the first round of combat only, the ones with reach weapons automatically go first. Then, the rest roll init and the round advances as normal. For rounds 2 and the following rounds, init is rolled as normal.
This has the advantage of recognizing reach, while still recognizing, as you mention, that once you close in with your daggers, that polearm may not be an advantage. Combat being dynamic, you simply roll initiative on rounds 2 and subsequently, which indicates whether the reach weapon weilder was able to move away a bit to take advnatage (reach weapon wielder won init) or whether the dagger wielder was able to remain in close combat (dagger wielder won init).
If this is the way you go, you can perhaps create weapon length categories.
Option A: 2 categories:
Long: polearms, long two-handed weapons (greatsword)
Short: longsword and shorter (including daggers, hand-to-hand)
Option B: 3 categories
Long: polearms, ...
medium: greatsword, longsword, flail, ...
short: hand-to-nand, dagger, hand axe (?), ...
(should the grearsword be long? Should the hand axe be medium?)
You could also have only 2 categories, but decide that hand-to-hand always goes last (or has a penalty to init). I see fighting hand-to-hand against an opponent with a weapon, as being quite a challenge, myself.