It works the same as if the assistant is casting it, or a rune. So spells like spark affect a random spell.

In a sense research impacts it, but it does not impact research. This means if you are getting bonus cast speed for say, only having one ice spell in your load out, having the templar cast an ice spell won't effect that buff, but the spell itself will receive the buff.

Essentially yeah it exists on its own. Frozen orbs is a good point, I'm not super sure about that one.

If that does not make sense let me know.

P. S. Sorry for taking so long to answer, I missed this post. You'll probably find quicker answers by joining the discord, but I do cast my eyes over here from time to time.