Incidentally our DM has used different rules to try achieve the same purposes of your (except point 3), while when I am the DM I use standard rules for all of them.
1. Our DM uses Initiative every round. It was nice at first, but later became annoying. Furthermore it messes up the special initiative actions and it is slightly more difficult to keep track of spells duration.
Your way has no consequences of these sort. Seems to me that you are just trying to decrease variance of the Init rolls, so to make them more often close to average. You can also roll 2d10 to do the same. I don't understand why are you concerned this much about occasionally rolling very low or very high Init: it really isn't important whether one is the last because he rolled a 1 or because he rolled 19 and everybody else rolled 20, it only matters that he's the last. IMHO reducing the variance has not much consequences.
2. This house rule balances the weapons more, since every weapon has at least a threat range of 2. If this is what you wanted to achieve then it's ok, but remember that in general it will make combat last slightly less and would empower weapon damage against spell damage. If that's ok for then do it.
Our DM increased frequency of criticals by skipping the confirmation roll, that is if you score a threat then it is automatically a crit. It is a very bad house rule IMHO.
3. I think this is a variant in the DMG (except that you can't choose, you always roll), and in fact there's nothing wrong with it, just that it increases randomness. If you like it, why not?
4. Different rules for rolling, but our DM uses fumbles too. I really dislike them, so I am very biased against it. They are funny for some time, then they lose their in-character fun and become annoying. Higher level PCs do many more attacks and are therefore exposed to more fumbles: your rule bases them to Reflex saves which makes them less likely at higher levels, but still you are going to roll many times for nothing.
If you really like the idea of fumbles, I strongly recommend you to add another roll in between: after a natural 1, let the PC roll a confirmation check (just like with criticals). It will require one more roll admittedly, but it will make them even less probable.