To install in a subfolder under your site root you should prevent web.config inheritance. This is achieved with adding <location path="." inheritInChildApplications="false"> to this place in your parent web.config.
Then you have to provide permissions for the database this Sitefinity project is using and you are good to go.
I have tested this scenario at my end and it is working with full functionality.
Since you are able to access your backend and see the top navigation the problem should be connected with some IIS configuration and handling of services. Can you please review the settings needed in IIS in order to host Sitefinity projects
. Can you also check are the services executing ( see attached screenshot )?
the Telerik team
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