If a caster takes an improved familiar with the Fey-Touched template does the familiar have the fey subtype? The template doesn't explicitly say it does, but this seems an oversight.
No. It's fey-touched, not fey.
Also, AFAIK, there is no fey subtype, only type, and changing the type of the creature being summoned would have quite a few knock-on effects.
I see. I suppose the same would be true for all of the other simple templates, celestial, fiendish, resolute, etc. as non of those mention adding a type either. The knock-on effects were why I was wondering.