Can I make a Mobile site with Muse and then go through PhoneGap?

Yes, you most certainly can.

If you want to keep your Muse compatibility do not do it through Dreamweaver though.

Export as HTML and the create a zip file with the contents. Go to Phonegap,s website and submit the app directly from there instead of through Dreamweaver.

I tried building an App through PhoneGap, but I keep getting a error when I try to create it for IOS.  It asks me for a key? Do I have to be an Apple Developer to create an App for IOS. I don't necessarily want my App going through the App Store, I just want my mobile site to prompt the visitor to click on a button to download the App to their home screen.

Thanks.

Yes, you need to be an Apple Developer on a Mac computer as well.