Situation: I have Lillia and Smoke Mirror hidden on a Battlefield A My opponent charms Lillia Fae Fawn on the Battlefield B, do she make a sprite due the movement, keeping the controll of the battlefield she left, going to the other battlefield? And can I swap the Sprite just created and Lillia back to the Battlefield A to make a situation where my opponent will have to deal with 2 sprites in the BF B? (One created due the movement and the other from the Battlefield A)

Yes on both counts. Charm only moves Lillia (it doesn't steal control), so her "when I move" trigger fires, leaves a 3/3 Temporary Sprite at A, and you keep control of A — then your hidden Smoke and Mirrors can swap that Sprite with Lillia, leaving the opponent facing two Sprites at B.

Sequence: Charm resolves moving Lillia A→B → her trigger goes on the chain (Closed State, so control of A can't be lost — Rule 187.4.c) and plays Sprite #1 at A. Wait for that trigger to fully resolve first (the Sprite must exist as a target), then play Smoke and Mirrors from Hidden (it has Reaction). The hidden targeting exception applies here (Rule 811.1.d.2.a): the first unit must be at the hidden battlefield — the Sprite at A — and Lillia at B is the legal second choice since "at a different location" can't be fulfilled at A alone.

When Smoke and Mirrors resolves: Sprite #1 goes to B, Lillia goes back to A, her move trigger fires again and plays Sprite #2 at B, and you draw 1. End state: Lillia at A (you still hold A), and B has two 3/3 Sprites — one from A, one from the second move. Note that Sprite #1 arriving at B applies Contested, so a Showdown at B will stage and the opponent will have to fight them.