1. Layout size itself doesn't matter, you can have 1000000px layout. The objects that you put on the layout are important.
2. It's much better to have one 500x500 px background sprite repeated a hundred times, than one 2000x2000 px sprite. That's why it's recommended to use TiledBackground for backgrounds.
3. It depends on too many factors. You should regularly check performance as you develop your game, and if you notice a big performance drop, fix it.