Is it possible to assign a plan to a client then edit/tweak parts of it for that client as opposed to it editing and changing the original template plan?

For nutrition plans, when you assign a plan to a client it creates a unique version just for this client.
Any changes you then make are specific to the client and won't affect the master template.

For workout plans, you assign a plan to multiple clients, and if you click to edit one of those plans, you will be asked whether you want the change to apply to all clients who have been assigned this plan or not. If you choose not, the system will create a copy of this plan so the master template is not going to be affected. In other words, you can bulk edit a workout plan or customize it on an individual basis.