Folder with question mark when booting including recovery partition on MacBook Pro 2010
The differing architecture shouldn't be a problem. If you installed Mavericks on a 2012 MacBook that drive should boot okay on a 2010 MacBook. If you are unable to boot into OS X and unable to boot into the Recovery then it suggests both are corrupted in some way.

Internet Recovery might be an option, but unfortunately for Internet Recovery to work on a 2010 MacBook it would have needed to have this early 2012 EFI Firmware ROM update installed. If your MacBook isn't offering that option then I assume that means it didn't receive this update.

Two options are, to create a USB installer for Mavericks and try reinstalling Mavericks on that same hard drive, or to buy another hard drive and install Mavericks using those instructions. I'd lean towards the latter, as if the drive failed a Hardware Test that isn't a good sign. Modern hard drive are designed to cope with a certain amount of bad blocks. If the drive has enough bad blocks that it failed a Hardware Test I just wouldn't trust it.

BTW There is also this free tool to simplify the process of creating a USB installer for Mavericks called DiskMaker X.