Hi Tim,
Your question is complex. I will answer the parts I can as best as I can but in general I just don't have the bandwidth to offer free support for complex integration questions. I feel it my duty to help people with basic installation issues but beyond that I'm just too busy to try and help everyone with these kind of questions that are specific to a project implementation for which I'm not being paid. To answer these questions would require me to invest more effort in asking you questions to get towards the details of what you are trying to do.
To integrate with another ASP.NET app, one of them (mojoportal or the existing app) would live in the root web site and the other would have to be in a virtual directory marked as an application in IIS. Yes there is a potential for Web.config conflicts but these can generally be mitigated as discussed in this thread.
For static html files that are just plain content I think you would be better off putting that content into the CMS.
If your custom asp.net stuff can be worked into UserControls you can integrate the functionality into mojoPortal fairly easy.
To me the benefits of a CMS are somewhat lost if you keep a lot of static content or just use the CMS for a section of the site. I would question why that is a goal or requirement as it seems much better to get away from that kind of mish mashed solution and get the full benefits of a CMS.
Hope it helps,
Joe