Great platest reviews! I'm glad you went with new players and not people who have been around the D&D block and can break the rules like a pretzel. That's important too but it's nice to get the other side sometimes. ;)
Although I think some of the issues you raised are fixed by the fact that these are intended to be 'advanced' classes, you offered good suggestions too.
Whose giving eidolons and animal companions items? That's pretty silly and is just blatant min/maxing. Eidolons can't use armor, weapons, magic items etc. As a DM I might let one use an item on certain occasions giving proper RP or situational justification.
But equipping your pet/eidolon like a 2nd PC? No no... that's just cheating. ;)
Summoner looks very cool! I want to roll one up! I always liked having cool pets. :)
The witch doesn't do anything for me, but that's not a fault of the class: I just don't care for the flavor of it. However for a player who wants to play a witch player concept, the design is really good for it. :)
Any Mr. Ed tricks would be a no go in any games I run. Animal companion or not, he can't write what he wants in the dirt. I don't care how smart he is. ;)
Maybe RAW it's allowed, but I wouldn't run it as such. Or ok if you really want to argue that it can write in the dirt with it's hooves fine... but your animal companion has the worst penmanship this side of the Mississippi. You've heard of chicken scratch, this will be horse scratch. ;)
And if you still want to argue that it can write long elaborate letters, than congratulations, you've discovered a way to min/max even animal companion linguistics skill. ;)