Are bracers of armor armor? No. They provide an armor bonus to AC, but they aren't armor. Items that qualify as armor show up in that portion of the book marked "equipment". So they work just fine.
For the robes, ditto.
Adding dodge bonuses? Normally, no. But if you look through the rules on magic item creation, there are rules for pricing magic items that boost AC in nonstandard (i.e. armor, deflection) bonuses.
No. Bracers of armor is not armor.
You can't enhance regular clothes with an AC bonus permanently.
No, a monk does NOT lose his abilities when he is wearing bracers of armor. As Wraithstrike and Lathiira said, this item is a wondrous item, not actual armor, even though it provides an armor bonus.
Armor bonus does not always equal actual physical armor.
Master Arminas
If you have a caster in the party, though, try to just get him to cast Mage Armor on you. Even if he makes you buy a pearl of power for it (a 1st level spell is really not asking for much...), that's still FAR cheaper than bracers +4. Bracers can go up to +8, but that costs 64,000 gp. I guarantee you that you could get many many more boosts to AC using that money to upgrade ring of protection, amulet of natural armor, dexterity boost, dusty rose iuon stone, etc... instead.
On topic of begging mages... Amulet of Mighty Fists is inaccesibly expensive. Monk can benefit from either Greater Magic Fang or Greater Magic Weapon, however. Basically, monks in general really need the support of a friendly caster.