To further explain the time server issue, there are set quests that can be done from 6am-6am EST. After that 6 am, a different set of quests takes over. Because of your time zone on your computer clock, it will show the active quests only during certain times (I can calculate those times for you if you give me your time zone). When not in those times, you are seeing either the day before quests, or the day after quests. The servers has limitations to prevent people from doing quests like that, so the system shows you they are there, but does not let you do them. Changing your computer clock to EST will force the system to show you the active day's quests only.
If that does not fix the issue, then we can progress further and look into other solutions. But judging by the 10 am and 10pm on your map time, I am pretty sure you outside of those time frames of being able to complete them.