In your journal you've got 3 tabs: Current Quests, Collections and Completed Quests.
The both unfinished quests you mentioned, should be listed in the Collections-quest tab (prop. Shard- and Red Lyrium-Quest).
I took a quick screenshot for easier understanding: http://i.imgur.com/GbhkElA.png
However, the cave you mention requires an Inquisition Mission (war table) to be done first.
More details in Spoiler
Spoiler
The Inquisition Mission is called "Red Templars on the Storm Coast" and will unlock mid to end of the games' act 2 (level ~14-18).
The Inquisition Mission will trigger the quest "Red Water" which will unlock the previously locked cave with the remaining red lyrium and shards - including the zones' dragon.
Cheerio,
Matricus
