- Are computers bothered by X-ray machines or anything else that carry-on or checked baggage is exposed to?
No. Magnetic media is not affected. That applies to undeveloped photographic film.
- What kind of red flags would packing a non laptop raise with the TSA?
Does it look like a bomb? Is it clearly accessable (openable)? Can it hide a bomb? I've seen CPAP machines receive swabs for explosive chemical tests because the TSA can't open it up to look in it.
Pack a regular bag if you can, and unzip it for them to look around. If it looks suspicious, then it is.
- Are there any setups known to work well for packing around larger system (like server scale)?
Unless you cook up a homebrew setup of some kind (dolly cart, etc.) you're probably going to have a hard time. I certainly wouldn't put a server though luggage, that's a sure-fire way to end up with a box of broken contents. Maybe look into packing a powerful, high-end PC class board into a portable LAN party case that doesn't have blazing dragons and etched tattoos on it?
- Has anyone seen one of these cases bands use to back there sound equipment used to mount a server?
Mobile 4-post racks, yes. Expensive, but if you do a lot of travel, it might be worth it. And you can certainly mount a 1, 2, 3, or 4u box. If you're willing to pay the price for this, be sure to include a UPS unit in it, there are several to be had that are rackmount-ready. Do this because you don't know the power situation ahead of time.