This is a total guess, but I'd assume running it from HD would consume more power. Not because the HD would need more juice, but because HD's run hotter, and the fans would probably kick in more often.
I do not normally run it till the battery dies, maybe once a month, just to cycle the battery
If I'm not mistaken, the 8887 has a lithium ion battery, right? Those don't need to be cycled (and, actually, *shouldn't* be cycled -- it will wear them out faster).
Both addresses you gave are for the Dell website, and your machine is probably just automatically checking for updates and patches. I'd hardly call it "spyware" based on the information you've provided so far.
If your WiFi coverage at school is questionable, trust me, you're better off with an external PCMCIA card than using an internal. They're nearly always much better at picking up lower-quality signals than internal cards.
I'm not surprised the Sager guy wasn't much help -- this really sounds like a wireless router problem, and not a problem with the Sager.
To answer your questions:
1. Is an 802.11g router so powerful that it will saturate the signal of an 802.11b router that is closer.
Maybe. 802.11g does have a stronger signal, so if the two are interfering with each other, it's not surprising the 802.11g router would win. Especially if it's a...
If you read Contacting Sager for Tech Support (Please Read) they don't want to use an outside resource for support but the fact that it was mentioned, well?
I think they mentioned it just to reassure people like you who'd rather not deal with overseas support, not because they're considering doing it.