When you share a project folder all analyses within that folder are now accessible by the people you have shared it to. What they see depends on the combination of two things:
The type of sharing that you define for them, either 'Can View' or 'Can Edit'
Their own user group permissions
Users must have both the ability to edit analyses and have an analysis shared to them with 'Can Edit' to be able to edit.
For example, 'Viewer' type users have limited access to Ipiphany. They cannot create or edit analyses and they do not have access to most analysis tools (Key Drivers, Relationships, etc). They can only open and view analyses. If an analysis is shared to them (even with 'Can Edit') they cannot edit the analysis or use any of the tools other than 'Insights'. They can also not open the dataset directly.
This is what they see:
