Can only admins use the {{blocked}} template on talk pages? I know that only admins can block users, but can non-admins give them a notice that they’re blocked? Please help me with this.

No. Admins always put the blocked template on the talkpage. No need for you to do it to.

It’s not always placed on talk pages, especially when it’s a spambot (because they won’t really see it), but yes, it’s only meant for admins to use.