[quote=@TheUnknowable]
Is there a way to:
Look at notifications that have been cleared from the "notifications" tab?
[/quote]
Not at the moment. Such a feature might be programmed in the (probably distant) future if the want for it by the member base is large enough.

[quote=@TheUnknowable]
Is there a way to:
look at a history of your like/laugh/thank list?
[/quote]
Only sort of list is the one on your profile that says how many you've given/received of each. It doesn't link. But you could try searching the thread for things like  like / laugh / Thank.