For 1: This may actually be related to issue number 2. Fix it first. For 2: When you change the visibility of the map, you need to trigger the map resize event: http://code.google.com/apis/maps/documentation/javascript/reference.html#Map
Also, I'm getting a couple of non-map related script errors on your page regarding jQuery and document.body. -- You received this message because you are subscribed to the Google Groups "Google Maps JavaScript API v3" group. To view this discussion on the web visit https://groups.google.com/d/msg/google-maps-js-api-v3/-/Zfe1hgjwVqYJ. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/google-maps-js-api-v3?hl=en.
