Are we allowed to use a custom sprite for the main menu logo? What about the game icon?
No;
1. For the logo you can use one of the fonts I've made, or a font from elsewhere with added effects. However if you'd like to include more to your logo it has to be sourced from the available game assets. As per the rules;
Sound files (sound effects and music) and fonts can be custom made or gathered from other sources.
2. The game icon has to be made from either the logo as described in 1. or from assets I've released. For a guide see here.