Hi Rochelle, it sounds like the user may only have "View" access to the Project(s) or other object type(s).
Not sure if you add Projects using Templates or not‚Äö√Ñ¬∂
If not, go to Project Actions, then click on Sharing. You will see list of people that have access to the project. Check to see what their access level is - if it is View, you'll need to bump them up to Contribute access to be able to give them permission to "Edit Custom Form" at the Project level. You can also check to see how your Project "Access" section is set up via Edit Project and make any changes needed.
If you use Templates, you can set up these access level permissions at the Template level, so that any Project created using the Template will have the applicable access levels set up beforehand (so that you don't have to set this up each time you add a project). You may see that people may only have View access to the project, which may be contributing to the reason why they are not able to edit Custom Form at the Project level. Terry Hynd EBSCO Information Services