1.) Is Explorer completely free? Work with small water systems and some of the systems will really only use it for viewing, and if so do they need a ArcGIS account to access? I was hoping I could make the map, and share it with them while not making it public so everybody can't see their assets without them being apart of our organization. Is this possible?
2.) What's the best workflow to get an already made ArcGIS PRO map onto both the desktop and mobile version of explorer for viewing purposes and keeping symbology/design etc..
Update: I realized making a mobile map package was quite easy and could view it on my ipad! although that is within my organization, and I am having problems trying to find how to open this same mobile map package on the desktop explorer?
Last I looked into it, about three months ago, desktop Explorer could not open local MMPK (mobile map pakage) files. I think it is on the developer's to-do list.
Explorer is completely free for users. As far as I understand, you can either purchase the Publisher extension which enables anonymous use of map packages (no logging in to an AGOL account), or each user will need at least a View Arc Online account, thereby allowing them to view map packages shared with the group/organization but not the public.
With regard to access and sharing Brian's understanding is correct. If you don't want the Mobile Map Package to be public, your map users will need a viewer account, so you can invite them to access the map through a private group.
There also is a version of Explorer for ArcGIS, currently in Beta that can be used on Windows 10 devices.