Sorry but I can't help with that.
1. VS design view is not very useful, it has never used the css from a site specific skin because at design time there is no sitesettings or http context and it cannot load css from the correct skin folder at design time, it can only do that at runtime when there is an httpcontext and sitesettings can be loaded and the code decides where to load the css files and theme and master page from based on site settings etc.
I recommend use the web browser for seeing the design not the VS designer, I only ever use source view in VS myself because the designer in VS is not very useful for me. But that doesn't mean to run it in the debugger for designing, that is way too cumbersome and slow. What I do is right click the /Default.aspx file and choose view in browser which will load the site in the browser using the VS web server (or IIS if you have it configured that way) without launching the debugger so it is much faster.
2. I can't promise the designer works, I don't use it myself because it is basically useless in mojoPortal due in part to the way we structure the solution and choices we have made about how to load skins at runtime to support multiple sites.
3. I have no idea why it works for you without errors in the designer for some skins and not others and have no way to troubleshoot that.
4. Lots of user settings in VS can be a factor such as whether you have html 5 validation enabled or xhtml etc. VS really should not treat server controls like raw markup (for validation purposes) and I don't know why it does that. I know that sometimes it doesn't recognize things right away, VS is a big beast and it runs lots of things on background threads and builds up a cache of items for intellisense that affect those errors in design view and those little underline squigles in source view but the squigles go away later after vs has built up all its internal object cache.
5. When you say you upgraded mojoPortal to 2.3.9.0 it sounds to me like you are using the pre-compiled release files in VS not the mojoPortal source code, the pre-compiled release files are not really intended for use in VS, they are meant for production deployment.
Hope that helps,
Joe