[RPG] Does magical ammunition stack with a magical weapon

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.

YES, a mundane arrow fired from a magical bow overcomes the resistance

In the D&D 5e Errata, this issue is addressed:

Magic Weapons (p. 140). The section ends with a new paragraph: “If a magic weapon has the ammunition property, ammunition fired from it is considered magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.”

Here are some additional reasons:

1. Jeremy Crawford says so. If this isn't enough reason for you, please read on.
2. In the weapons table in the PHB (p. 149), 1d8 is listed as the damage for a longbow, not for an arrow. Bows are weapons that specify that they require ammunition, and arrows are ammunition, not weapons.
3. The resistance is against "bludgeoning, piercing, and slashing from nonmagical weapons" and if a +1 bow is a magical weapon, the damage bypasses resistance since it is from a magical weapon.
4. A single +1 arrow is in the rarity category "uncommon", just like +1 bows. If an archer is relying on +1 arrows to be as relevant in combat against a nonmagic-weapon-resistance enemy as a melee fighter with a +1 weapon, the archer is only going to have a handful of one-off shots for their entire career if item rarities are followed from the 5e DMG. This will severely limit bow users at later levels while melee users and casters are able to do full damage. The alternative is that the DM has to give out stacks of +1 arrows, which breaks the suggested occurrence of magical items.
5. According to the "Effective Hit Points Based On Resistances and Immunities" table on page 277 of the DMG, as CR increases, the effective hitpoint multiplier of a monster with immunities and resistances decreases. The claim made in the text above this table is that the change is because, as characters increase in level, they should have access to better means of bypassing the resistance or immunity. In the case of an archer, the small collection of magical arrows that they may collect in their career (again, as per rarity suggestions in the DMG) may last a couple of encounters, but doesn't represent "the means to counteract that resistance or immunity" after more than a couple of encounters with relatively common creatures at higher levels (basically anything incorporeal, many elementals, many constructs, many creatures of magical nature).