You can transfer some paid apps from your phone (or the emulator on your PC), but, some are protected and the apk can not be backed up, some "phone home" for a license check - without market they can't validate you own the app, some have a EULA - prohibiting copying and others just flat out won't install - due to our devices limitations (in this case you lose the $ - unless you wanted it on the phone too.)

In regards to the apps offered on the market using the emulator - you are only shown those apps which run on Android 1.6. Any that are exclusive to higher versions of Android are hidden/not offered.

I keep AppBrain installed as a quick way to check for apps needing an update.