The "how to" websites don't tell you, but after you have downloaded the current.gpx map file from your old Garmin to your computer, you need to rename it as temp.gpx. Then when you upload it to your new Garmin the new GPS will know what to do with it. I found that info on a blog. Once I renamed the old gpx file, and uploaded it, my new Garmin 2555 took it and applied all my waypoints (saved places) as it should.
No, you can not upload a Google map. But go to the Garmin Web site and download BaseCamp. You can use that software to create maps and upload them. BaseCamp is not as easy to use as Google but you can do so much more with BasCamp than you do with Google.