Don't buy the blue shards with Gems. You will get some while farming, and as rewards for various quests, missions, challenges and such. Also during events and tournaments.

Keep your Gems. If you want to quckly have a strong champion, your starter champion may be worth buying the Masteries for 800 Gems when you get him/her to *6 level 60. It depends on your starting choice, though.

If you're going to do that, at least wait for the next 2x ancients event so you're likely to get a couple of epics out of those 11 shards. At normal times, I don't think that's worth blowing all your gems on - even if you get lucky and pull Apothecary or Frozen Banshee (most of the other super good rares are voids, sadly). 

The gem mine is a big investment, but it pays itself back after 100 days and after that it's free gems every day. Obviously that's less helpful right now, but better in the long term for your account. 

thanks guys, I guess i will spend it on something else than haha :)

since i got my valkyrie through an ancient shard i have to much faith in these shard even though I didnt get lucky since :(