when touch the left or right arrow, blocks the other movement. causing lacking in the response.

We need a Main menu like first Screen in our game, through this we could go into the
Play Screen (where a level list appear), Option Screen (to select controls, disable/enable music and fx,...) and to click on exit to exit the game.

If I push the up button, the main character should jump

We need to have a class with all common thing about levels. Then each level extends that class adding their particular implementations.