Welcome to the Forum and congrats on what seems to be a really nice car.

Great description but it may be difficult for us to help with the diagnosis without actually hearing it. You could try to post a video with sound and that may help out. Reason I say this is that these cars actually have a common ticking noise (many mercedes do). Some will say it might be the fuel injectors. Others may have other thoughts. I have the "tick, tick" noice too, but usually you can only hear it appreciably at low idle and / or when the hood is open. What side of the engine is it coming from? I've identified the noise from the drivers side near the wheel well fender area.

As far as the miss.........no pun intended but it will be a hit or miss diagnosis. Lot's could be causing that, even a loose vacumn hose.......... but, you should do a search on here for similar symptoms and see what pops up.

The hard shut down also seems to be common. I'd have to say mine does that too, but it's only hard by my standards, I don't think anyone else might notice it or say it they feel it. It's just something I notice in comparison to my other cars. May not be anything to worry about on this issue.

Good luck with everything. One word of warning though, if you are taking it to a GM dealer, I'd be very warry of them being able to work on these cars. Heck, I even have my worries with certified Crossfire mechanics. I haven't found any that are all that good.............