@mark2410
Apple does not allow user control over bitrate? I mean, come on, Apple lets you convert your music into a gazillion different combinations of codecs and bitrates. Just not for the "on-the-fly" conversion for the small size iPods. Apple let's you have 100 versions of the same song to sync YOURSELF to the iPod.
This is a function for the 99.9% of people who want more songs on their iPods but want higher bitrate ones on their desktops (as purchased). Nobody stops you from doing the conversion yourself and sync as you please. Apple does not prevent that. They ADDED this functionality, nothing was taken away from you. That in your case this functionality does not suit your need only means you have to do it by hand, which Apple fully supports.
That this is in your case not what you want is sad, but there are plenty of workarounds. You can for example create a complete new library, just start iTunes and hold the option key while it boots and you can choose your library to work with. You could use aangens example and create a mirror image of your library and convert it into you desired bitrate and sync your shuffle from there.
It's a bit like your car dealer gives you a sunroof for free and you complain that it's not a convertible. :-) After all, itunes is a free software that you can use totally for free to organise, convert, rip, burn and and and your songs, even if you will never have an Apple ID or itunes account. And for a free software it's quite cool me thinks...
To your questions about authorized computers:
there is no way to check a list of you computers. However you have the possibility once in 12 months to de-authorize all and re-authorize the ones you really need. It is important to de-authorize a computer before you sell it etc. otherwise you have to use the once in 12 months option when you reach the 5er limit. Reminder: amount of iPods/iPhones/iPads to sync with is unlimited.
so long,
K