^ Definitely not a design feature.
Get 'em to look at it. Very occasionally, I'll get a random loud static sound out of my speakers. Usually, it only happens in the super cold when I drive to Maine in the winter. I assume it's just a loose wire somewhere. It's too intermittent for me to deal with it.
Pulls to the right is just an alignment issue. Get an alignment and you'll be good to go.
Brake issue may just be some build up/deposits/glazing on your rotors. You can try bedding them in a little bit to clean 'em up. Basically do a couple really hard slow downs from ~50-60 down to about ~20. Do it somewhere where you can do it safely without somebody behind you.
Is that Atlantic Blue Pearl (tough to tell in the pic)? Best color choice, imo.
That is a pretty high price for an '05, but that is ridiculously low mileage for one also, so I'd say reasonably well bought.
Don't know how much you've read about the 05s by now, but in case you haven't already found out heard about it, the 05s do have a couple fairly minor known design flaws. First is that there is a banjo bolt with a filter in it in the turbo oil feed line. This is designed to keep the oil in the turbo extra clean, but it has the potential to clog up. If the filter becomes clogged, it can (will) lead to oil starvation of the turbo ... which is bad.
You can check the filter regularly or remove it. Search here for lots more details.
The other poor design choice has to do with an extra catalytic converter in the up pipe (ahead of the turbo). This was originally included to help with cold start emissions, but if your exhaust temps spike too high, it can cause the cat to melt and send metal pieces through the turbo ... which is also bad. A used sti uppipe (search here and nasioc) is the best value on replacing the up. However, you can get a nice new one for ~$100 - ~$125, so this is a pretty high return on investment in terms of piece of mind/preventative maintenance. No tune required for just an uppipe. If you down or intake though, you'll definitely need a tune.
Enjoy your new LGT! They are awesome.