1. Assuming you are still running scans, you can see the most recent results in the scan log. You also will see repeated entries in the shield logs for a machine that has something that was detected but not cleaned. I don't particularly like the infected machine report because by default it shows things like URL:Mal as a threat that has been detected. not really useful.
2. It will cancel the job. There is a setting in the scan job to wake the computer up for the scheduled job. I'd recommend using this option and scheduling it at a time when someone is unlikely to be in the office (2am?)...
3. I'd spend some quality time with the computer in question. don't rely on the console for that.
4. There is an option under the network group settings to download from the internet when the mirror server is not available. I'd like to see you get the mirror working, but if you really don't intend to use it you should stop the mirror service so the clients don't connect to it and get a response that falsely reports the old version they are running is the latest (the one from months ago that was the last one the mirror downloaded).
5. I think this is more related to the scheduled scan jobs than the group settings. One mistake people make is that they delete the full system scan job and expect it to stop running as scheduled on the client machines. It doesn't work that way. Think of it as a template that the server holds. When you change job settings, you publish a new template for the workstations to use. If you delete the job, you delete the server copy of the template, but the clients still will continue to run the last valid version that they had downloaded. If you want to stop a scan job from running, leave the job in the job list, and change it's frequency to one time, and change the date to sometime in the past. The clients will download a new version of that template, and behave accordingly.
I'd recommend still running the full and quick scans, but doing so with the wake PC option, and scheduled for some time in the middle of the night.