iPhone backups?

ok, i hope i get the answer i'm looking for. PART1 will be my question, PART2 will be the particulars of my setup, PART3 the backstory and why i'm asking


PART1 ; Where does mac osx 10.8 keep iphone backups?

PART2 ; I have always kept my itunes library and folder etc on an external drive, so will the backups be found there by chance, or on the native internal drive of the OS?

PART3 ; For no known reason my iphone was beginning to act strange, then it started rebooting/ shutting off at random etc. eventually getting to the point where it would only come on if it was on a power supply. after opening it up it appears the battery connecter to the main board was coming loose at the solder joints

so i backed it up and tried to re solder the connection to no avail and with no result. may have even made it worse because eventually it just started going to the apple logo and then off and only on power supply.

so i ordered a replacement iphone should be on its way, BUT last night i was in bed and couldn't sleep and all the sudden heard my imac clicking for about 30 secs. i didn't think anything of it till i woke up to put on music and check the weather. it was frozen. reboots brought me to the flashing folder w/question mark. HD is dead. data recovery 3 and disk warrior don't seem to do anything for it.

my iphone had pictures i cant get back as well alot of other invaluable data.
if i do a clean install on my iMac w.fresh hard drive my itunes will run off the external as it always has, even the library xml (xml?) is kept there, does that mean my iphone backup is safe and sound?

 

thanks Foxfifth, that is what i was afraid of.....