Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
First go to Apple > System Preferences > Date & Time. Click Date & Time tab. Enable "Set date & time automatically" and correct time zone there.
Go to Applications > Utilities folder and open Disk Utility. In Disk Utility, select your hard disk in left column (Macintosh HD), then Repair Permission. After that click Verify Disk and if asked to repair, click Repair Disk. If you are using 10.11, then click First Aid button in Disk Utility and run it.
Then go to Apple > System Preferences > Dock and turn off "Automatically hide and show the Dock" option.
Re Startup Disk full issue, you have to delete unwanted files from your Mac and empty the trash. Delete musics, movies, photos, videos etc that you are no longer need and empty the trash.
Let me know the results please.