Hi,
mojoPortal is not an editor for html files, content comes from the database and skeleton markup such as the DocType come from the layout.master file of the skin, so you could change the DocType there if you want.
The w3c validation error you got about invalid script is caused by the defer attribute which should only be used with external javascript files. This was a minor bug in a previous version of mojoPortal but was fixed quite a while back so you must have an older version of mojoPortal installed. Changing the DocType will not fix that but upgrading to a newer version of mojoPortal will fix it.
I think you made a bad choice to install mojoportal in a sub folder named mojoportal and redirect to it. You should have installed it in the root of the site. Even if you have an old classic asp site running in the root, you should be able to install mojoportal on top of it, there is not likely to be any file collisions. Then you would just redirect from index.asp to Default.aspx and add Default.aspx as a default document with a higher priority than index.asp
I also think you are confused about how to get google to index your site. It has nothing to do with any API key, that is only for google analytics which is useful for you to track site traffic but has no affect on google indexing your site.
To get google to index your site you need to submit your site map(s) to google webmaster tools as described here:
http://www.mojoportal.com/search-engine-optimization.aspx
but if it were me I would not do that until after you move the site to the root. Having mojoportal as part of your url is not as good for SEO as it would be if you run as a root web site.
Hope it helps,
Joe