Can someone with Magery 0 use a missile spell enchantment on an item (e.g. Sunbolt)

The key words are Swift and Next Attack

Swift Actions
In D&D3.5e, you may only perform one swift action per turn, even if it is a mental action. So, you would only be able to activate Dislocator once per turn, at the most.

Next Attack
Multishot and similar abilities and effects produce additional projectiles as additional attacks. When you're firing two arrows, you're really making two attacks. So the one you designate as the "first" attack will be the "next" attack for Dislocator. Even if you could activate it more than once per turn, you'd have to activate it before each attack, meaning it would have to be in-between the arrows produced by Multishot, which isn't possible.

I really liked this question because of the idea of the idea of hitting someone with so many arrows that they poof and appear in the air, but unfortunately, it's not possible with that set up. Alternatively, you could hire four wizards of sufficiently high enough level to simulate the effect in battle.

"Look at what my arrows did!"

The four wizards are high-fiving each other in the background while looking mentally exhausted.

Edit: One thing I neglected to mention is that Dislocator mentions your next "successful" attack. Meaning that if your first three arrows miss and your fourth arrow hits, they would have to make a Will save. Still, you cannot force your opponent to make more than one Will save per turn in this way.

1. Your pricing of the small masterwork light repeating crossbow is correct.

   Your pricing of the continuous master’s touch is correct per the guidelines. As a DM, I might not be so sure I like that price, however.

   Your pricing of the at-will use-activated magic missile is correct. However, it would not fire missiles that deal 3d4+1 damage, as you seem to imply. It would instead fire three separate missiles that deal 1d4+1 damage each.

   You have a mistake when you add them together: firstly, you dropped the \$\times2\$ multiplier from the duration note on master’s touch: it should be \$10,000\text{ gp}+4000\text{ gp}\$, not \$+2000\text{ gp}\$. Moreover, you missed this note:

   Multiple Different Abilities

   Abilities such as an attack roll bonus or saving throw bonus and a spell-like function are not similar, and their values are simply added together to determine the cost. For items that do take up a space on a character’s body each additional power not only has no discount but instead has a 50% increase in price.

   For one weapon with two different effects, you need to pay half-again the cost of the continuous master’s touch. So the cost should be \$10,000\text{ gp} + \left(4000\text{ gp} \times 1.5\right) = 16,000\text{ gp}\$.

   Finally, Eberron Campaign Setting has a page (268, to be precise) on warforged components. It includes statements like

   A warforged component usually occupies the same space on the body that a magic item of the same kind normally would.

   Likewise, armbow specifies that it

   attaches to the arm of a warforged, completely covering the hand.

   So assuming that this item uses up your character’s hand like the armbow does, it should cost \$16,000\text{ gp}\$. If it does not,

   Components that do not occupy any space on the body cost twice what they would cost as ordinary magic items.

   Thus that would be \$16,000\text{ gp} \times 2 = 32,000\text{ gp}\$.

   Either way, the fact that the base cost is less than the price of the armbow, despite having significant extra features, suggests to me that your DM may very well dispute these prices. I would.

2. A magic weapon must have a +1 bonus on it before receiving any other special weapon properties. But you aren’t enhancing this as a weapon, you are treating it like a wondrous item. The rules don’t really cover this possibility; I would probably require the +1. But a +1 is all you need; after that, you’re free to put as much other magic on there as you want without needing a higher enhancement bonus (with the exception of the more powerful weapon augment crystals).

   Any enhancement bonus on the item would add to attack and damage, yes.

   For costing these, the fact that you’re adding features to a magic weapon means that you need to consider that 50% premium again. You have a \$10,000\text{ gp}\$ component (the magic missiles), a \$4000\text{ gp}\$ component (the master’s touch), and a \$2000\text{ gp}\$ component (the enhancement bonus, assuming you go with the minimum +1). The second and third each cost 50% extra because you’re combining them on one item. Like so:

   $$ 10,000\text{ gp} + \left(4000\text{ gp} \times 1.5\right) + \left(2000\text{ gp} \times 1.5\right) = 19,000\text{ gp} $$

   This adds onto the \$550\text{ gp}\$ cost of the base item, so your total is \$19,550\text{ gp}\$. Again, twice that if it’s not taking up your hand.