1, I assume by power lead you mean the USB lead that came with the GPS? if so it is not a power lead but allows you to connect to the gps via your PC using Basecamp or Mapsource to load tracks etc, or as a USB device. to power the GPS you need a different lead that is wired slightly differently.
2, Did a manual come with the unit if not one can be downloaded/ viewed here. http://www.gpscity.com/pdfs/manuals/62S-EN-MANUAL.pdf
It should also be available at the Garmin.com site, but the link to the Manuals seems broken at the moment.
3, Although I don't have the 62s/st model from experience I would expect good alkaline batteries to last about 8 hours use.The battery saver and backlight settings can be changed directions are in the manual. Have you fitted the Micro SD card that may have come with the unit and contains a set of Maps?
Hope this helps a bit.
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