I've got several templates and everytime I try to apply a template, the addon buttons grey out and the process gets stuck. After a /reload I can use talented again.

I had the same issue, but I just feel like Talented need some times to set up the template into the actual talents. I noticed this because applying the template assign a random number of talents and reloading freezes it. But when only few talents are missing, the process ends fast.

So I think you should try by just waiting some times when you apply a template.

And maybe the developpers should add a pop up saying that the points are being apply and it takes some time.

The way it's meant to work is that it shows you your current talents, so you can see them being applied. I've just had some other addon-breaking things to fix before fixing that (like the lack of LFG role icon).
Sadly, I haven't had time to login to the game since WotLK released, so I haven't gotten around to fixing this yet

I have this issue every time I respec. Has anyone has any success getting Talented to fully apply templates?

I am having this issue as well. The addon applies some of the talents and then freezes.