Hmmm, not sure on the startup, but on the sleep angle...
Well first...
Bootup holding CMD+r, or the Option/alt key to boot from the Restore partition & use Disk Utility from there to Repair the Disk, then Repair Permissions.
Then maybe...
See if it's related to this...
The 2012 macs (and later apparently) not waking normally from sleep after hours being in sleep. (noted here ...
http://www.xlr8yourmac.com/archives/feb13/022813.html#2012macswontwake
"Why 2012 iMac/2012 Mac Mini won't Wake After Hours of Sleep (Hibernates/Powers Off)")
The sleepimage file still reappears even if never slept. Delete it (hibernate off, etc) - within minutes its back.
A note on that here - http://www.xlr8yourmac.com/feedback/Chameleon_SSD_Optimizer.html
About iMac sleep...
http://forums.macrumors.com/showthread.php?t=1529750
Try this: "sudo pmset autopoweroff 0" and "sudo pmset standby 0"