Boot from External Drive and New HDD

Hello everyone, I've basically 2 questions, so first I going to introduce you my trouble (My english fail sometimes : D)...

1- I've one MBP and one iMac Mid 2010 (like this http://support.apple.com/kb/SP588?viewlo...), and the second started to crash, something like S.M.A.R.T problem. So I search in interwebz about this and I saw that isn't a way to fix it. So the first question is Can I buy this HDD "Seagate 3.5" ST2000DL003 2000GB 5900 RPM SATA 6.0GB/s Desktop Hard Drive" to replace (in Apple Care). The size's right and this RPM is ok?

2- I installed a ML version in my external drive (connecting in my MBP) and It booted fine, for a moment I was a glad guy, so I restarted the OS in original MBP HDD and ejected the "External Mountain Lion" to plug in iMac and try to use. But when I try, It doesn't boot, just Apple loading screen, but I can access the 10.8.2 recuperation application (both, original from HD and the External too...), moreover I've a Bootcamp partition running win 7 perfectly. So I don't understand how can I start the recuperation application and win7 bootcamp, boot the External ML in my MBP, and I cannot boot the "External Mountain Lion" from external drive in iMac?