I was on the phone with a friend yesterday and he was asking about the air charge intake temps. I didn't really pay too much attention to them, given the relatively low boost I saw in my tests. But I did go back and look at the logs. The IATs while running were actually cooler than with the electric turbo off. Ray (another friend of mine - the guy who does my dyno testing), mentioned one of the advantages of this system is the lack of a need for charge cooling. With most systems, the compressor gets hot and stays hot. Turbos because they're physically connected to the car's exhaust, and superchargers because they're always spinning. And when a supercharger is always spinning, and dealing with a low volume of air (throttle closed or mostly closed), the air gets heated, even when not in boost. And that warms the compressor. In both cases, when boost is called for, both types of compressors impart their heat into the intake charge. Not so with the electric turbo. If you can keep the volute around ambient temperature, it'll function as a charge cooler itself. Coupled with the fact that you need about half the boost to make equivalent power, it's a win-win.
Conclusion: an intercooler isn't necessary, and in fact, since intercoolers are a restriction, would actually hurt power. If you really are concerned, know that you always have meth injection available as an option. In my case, at the track one of the things I'd try is just putting a bag of ice on the volute. That's an old school trick we used to do back in the day on 5.0 Mustang intake manifolds. And it worked quite well.
As for the alternator, I run a 200 amp, 3G style unit. It really only needs two wires - a power wire and a sense wire. The sense wire provides voltage feedback to the alternator. You can jumper the sense wire to the output stud. But then practical voltage for the car is lower due to cable losses. Or you can jack up the voltage by running the sense wire to the lowest voltage point of your electrical system. Just a thought.
Of course, that won't help much at idle. You can also put a smaller pulley on the alternator at idle, or just get a bigger alternator. Or just have the charging cut out at idle. There are a bunch of options. In my opinion, none of that's a deal breaker. I doubt you'll ever be in boost long enough driving around (or racing on a road course, even) to run the e-turbo batteries down very far.
Another thought - I run a 100ah LiFePo4 car battery now. It's smaller and lighter than the 32 amp hour lead acid battery it replaced, and while a lead acid battery's only got about 50% of its capacity that's usable (voltage drop), about 80% of the LiFePo4's battery is usable. Putting one of those in your car would be a win all-around - I figured I could charge my e-turbo packs 6-8 times between passes at the track before I'd start to be concerned about the car not starting. That's a pessimistic estimate, BTW.