Those specifications describe the vast majority of WP themes.

You can pretty much use any theme for that, but if you really want a flexible theme, I would recommend a Thesis theme.

Well said Antonio - I can't think of any premium theme which doesn't offer this benefit.

There are lots of free themes that are responsive and has custom menu however, you can also go to a membership site where they offer premium themes just coz it also guarantees support if needed.

If you are looking for Free theme, you can search there are lot of free themes available. If you want custom theme, you can have lot of more options based on your requirement.

Any theme on wordpress! You can customize any menu to how you want it to look.
Look inside a CSS file if you want to change font sizes or the colors and even animations.