Can the exported files be used for something else?

Yes, of course. Icons can be copyrighted resp. by Wube or mod authors.

What is the size of the tiles of the sprite map?

Tiles are 72×72 px (64 + 2×4 padding).

What is the format of the JSON file?

A PluginData object as defined in board.ts, simplified below:

type PluginData = {
    name: string;
    symbol: SpriteRef;
    boards: [MainBoard];
    spriteMaps: Record<string, SpriteMap>;
}

type SpriteMap = {
    path: string,
    width: number,
    height: number,
    padding?: number;
    cols: number;
    rows: number;
    index: Record<string, { row: number, col: number }>
}

type SpriteRef = {
    spriteMap: string;
    sprite: string;
}

type MainBoard = {
    name: string;
    symbol: SpriteRef;
    byRow: (Keyboard[] | Record<string, never>)[]
}

type Keyboard = {
    name: string;
    symbol: SpriteRef;
    content: Cluster[];
}

type Cluster = {
    cluster: string;
    name: string;
    symbol: KeyCap;
}