It's been a few years since I looked into it, but unless things have changed, you are supposed to send the unit to Polar when the battery needs to be replaced. If you do it yourself, you void the warranty.

However I never did that. When the battery died in my chest strap, I decided I didn't need to use a HRM anymore so I never had it replaced. And for the watch/cycle computer/HRM, I was able to find a watch repair place that replaced the battery for me. It's not a common battery size, so it was hard to find a place that carried them or would order one for me, and it wasn't cheap.

As for GPS, I would think the only way to measure distance while running is with a GPS or a pedometer, and the GPS is probably more accurate.