I was thinking of making a mage that uses Illusion and Conjuration, do these two skills work well together? I usually just go with destruction and alteration but thought I might go with a different set of skills this time.

Yes, any set of magic skills can be used together and in my opinion illusion and conjuration are the best two, but i would recommend still using the alteration skill for mage armor because as a mage your going to be wearing mostly robes anyway and at higher levels you can be easily killed without some form of armor or defensive magic.

Another question could be; do Courage and Call to Arms work on Conjured and Reanimated minions?

Yes, I think I'll still use the alteration spells for defence and magic resistance. The plan is to use illusion to fear/calm and use minions to kill enemies with me supporting with bound weapons. Hopefully it will work out ok.

Don't take the Atronach Perk in Alteration along with Conjuration. It makes you disappear when you try to conjure and you're vulnerable for a couple of seconds, plus your conjured minion doesn't appear.

Illusion and conjuration work great together. I would even add that sneak is a perfect fit for the both of them...especially if one is playing as a mage with little health to spare.

Indeed and there's a http://skyrim.nexusmods.com/downloads/file.php?id=3352 for this. Nevertheless, Bethesda should correct this for all platforms, in the next patches -after all, it's all about flagging the spells not to be absorbed.

There's a mod to fix that problem. Thanks for the link, makes the Atronach stone worth taking.