Is it possible to show the creator of card on the card, so, that I don't have to open the card to view who added it?
Or is it possible to automatically add the creator as a member when a card is crated?
Neither thing is a built-in feature of Trello. In fact, the second question came up before, with the same answer:
You may want to submit a feature request to Trello (to have an option to show card creator on front of the card), or look into 3rd party tools such as Zapier to automate the self-assignment process.