Is it possible to create a project template which is using the templates on the network folder?
This would be nice, because the changes in the templates would be synchronized across all team members.
If you mean "add new file" will use a dedicated file which will be different for every template no.
Although you can struct your templates to have that feature a bit manually.
"Template" in altium is pure copying of a file or a project. Any settings must be included in this file-project.
By adding a file (lets say a .sch) in a project template named "Template.sch" designer can change AD default preferences to link on that file which will be unmodified during design and every time he adds a new .sch he will make a copy of the template which will be located on the same project folder.
He (designer) must change his preferences each time he works on a different project but it will be much easier to locate correct file template (because it will be inside the project he works on) for each project template and will be a simple point in TODO list before creating a new project or modifying an old one.
Also in this way you will have "Template.sch" on old projects for reference or mods.
In a same way you can include .preferences files which are the global AD settings.
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If you want to have 10 .sch in a project which will be based on a template, just add a 10 .sch in the project template and use a .sch template while you creating the project template.
There are no links or live update, just pure copy and paste.
If any part sounds weird tell to use examples.