8) Should be made optional for advance play only as this character can easily overshadow *any inexperienced players and can put off new players and possibly collapse the GM. We lost a player on his first session due to gross exposure of the synthesist (all night long) XXX
How funny. As a looooong time GM and player, here's what I take from this.
As a GM, you didn't check the character PRIOR to allowing it in your game. Your bad.
You apparently ignored that the class is in the ADVANCED PLAYERS GUIDE (not Core Book) and on top of that, is applying an Archetype template. Your bad as a GM again, especially since you make a point about it needing to be an ADVANCED class. (Your point above.) I fail to see how this is anyone's fault but yours as the GM for not knowing this ahead of time.
There are also some funny mechanics here. Some of the feats you referenced in your first post are obviously third-party, which means again as a GM, you haven't been proofing what you allow in your game. That's your bad again.
You aren't handling the class correctly. First point: they don't use stacked hit points.
--"The synthesist gains the eidolon's hit points as temporary hit points. When these hit points reach 0, the eidolon is sent back to its home plane."
So once the Eidolon goes bye-bye, then what? You have a crunchy caster again, with less casting power than a Wiz or Sorcerer. This is NOT the same as stacking hit points, and should not be handled like it is.
Second, losing the Eidolon. The fused Eidolon still goes away when the Synthesist sleeps, is KO'd, etc. So there's that to consider. (everyone has to sleep,

) There's a level 7 Summoner in my group that I GM for, and guess what? I single blowdart with a DC20 poison save knocked him and his Eidolon right off the board.
I'd also like to point this out: "The eidolon has no skills or feats of its own." - This is unique to the Synthesist Archetype. So that means your Eidolon doesn't get all those fun extra feats of its own, so where is your player getting those? If he chooses feats for himself OR his Eidolon, those are static. They don't change via Evolution (unless I missed an ability in my reading somewhere)
Then there's the fact that the Eidolon is still exposed to things like Banish: "Spells such as banishment or dismissal work normally on the eidolon, but the synthesist is unaffected. "
So now how awesome is the flying Synthesist when his Eidolon gets banished mid-flight? Not very.
All in all, I'd say that there are class balance/imbalance issues everywhere if you look hard enough. The trick is finding them BEFORE you allow them into your game willy-nilly. It's unfortunate when a player has to pay the price for a mistake that the GM made. (Or a series of them.)
And finally, really? This is a game of IMAGINATION. (cue rainbow here) If you can't think your way around a lone min-maxer in your party,that's sad for someone who's been playing since '77.