I'm not a new player, but I have been questioning this for a long time. A long time ago I thought I saw a few staff's with two school abilities? (Example: A staff with life or Ice 0 pip cards) Is this a thing? I've been trying to research this but I've had no avail, it's a silly question but I'm desperate to figure this out!
Yes, many off school wands (majority of them being crowns only) now carry wand attacks representing two schools.
Some even have up to three or four!
Also, some of these wands have "may cast abilities" which works similarly to how a pet's talent works. It's trigger is using the wand attack provided by the wand to attack.
So, occasionally, you will cast two attacks in one turn.
It is a thing. One of my wizards has a wand that has zero pip wand spells in both ice and shadow school. I haven't gone looking for one that is both ice and life, but there may be. Have you checked for it in the crown shop? I suspect they don't go into the Bazaar, though they might drop in higher level fights.