from what I can tell your system is lacking all of the custom Asus driver updates for your system dated after 8/22/2013
go down the list and install them and reboot
http://www.asus.com/Notebooks_Ultrabooks/ASUS_ZENBOOK_UX302LG/HelpDesk_Download/
I think one of the old asus drivers is stomping on some of windows kernel memory structure.
It is more likely a direct root cause of your various failures.
most likely because of the type of failure, it will not be your actual hard drive. (the input output from the drive did not fail, the data stored in memory was corrupted, easy to do with a bad driver)
BugCheck 7A, {1, ffffffffc0000005, ffffe0013530b900, fffff6fac000c000}
KERNEL_DATA_INPAGE_ERROR (7a)
the current process was sdiagnhost.exe (it think it is Microsoft scripted host diagnostics)
basically the system keeps a map of how it maps your physical RAM to your pagefile.sys
and the map was corrupted so the virtual address it got from the table was invalid and the system called a bugcheck.
the system tried to page from address fffff6fac000c000 but could not because it is a invalid pagetable entry
for a error like this you would confirm memtest86 works on its own boot disk.
if it does run without failures then you have to:
run verifier.exe and set global debugging flags
see
http://www.sevenforums.com/crash-lockup-debug-how/65331-using-driver-verifier-identify-issues-drivers.html
then set your memory dump from a mini dump to a kernel or full memory dump
reboot and wait for the next bugcheck
with a mini dump the proper debugging info is just not saved to figure out the cause of the bad page table entry.
verifier.exe may catch a process that is corrupting the page table entry (if it is a driver corruption), or it can be faulty hardware
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looking at your driver list you might remove this file
C:\Program Files (x86)\ASUS\ATK Package\ATKGFNEX\ASMMAP64.sys Thu Jul 02 02:13:26 2009
it is a asus hot key driver. it is very old. the rest of your drivers have a reasonable file date.
you have the driver
\SystemRoot\system32\drivers\AmPeStor.sys Mon Oct 07 02:18:33 2013
Alocr Micro PCIE Card Reader Driver. there is a update to the driver on the asus website
this driver is not in widespread use. install the 2014 update under card readers
http://www.asus.com/Notebooks_Ultrabooks/ASUS_ZENBOOK_UX302LG/HelpDesk_Download/
also update your asustp.sys (asus touchpad driver) lots of bugchecks caused by the version you are running
\SystemRoot\System32\drivers\AsusTP.sys Tue Sep 17 02:28:40 2013
get the version dated 4/24/2014 on the asus website.
Look through the list of updates on the asus website. your system files are mostly from 2013 but asus has more current driver fixes. Any of these older drivers could corrupt memory of the other drivers and cause your failures.
basically it looks like you need all of the asus updates dated after 8/22/2013