Thanks for using Lunascape! Sorry you're having problems with it.
About your first question, could you give us the explicit URLs of a few pages and images for which the context menu fails to appear? Also, which engine are you using (Gecko, Trident or WebKit)? This will help us in our investigations.
About your second question, we have been unable to confirm a problem with the downloads. Could you tell us which language version of the Lunascape browser you are trying to update?
If you want the English version you could try downloading it via the download button on our site www.lunascape.tv.
You can download other languages from the page https://sites.google.com/a/lunascape-inc.com/en/products/web-browser-pc/orion.