I think all cards should be able to appear in your starting hand. If a card is problematic, you should fix the card, rather than make special rules to accommodate it.
Mirror - The issue is that, currently, Mirror can’t be played as your first card because it has nothing to mirror. This give you a big disadvantage if Mirror appears in your starting hand. One solution is to allow the Mirror to mirror nothing if it played as the first card. Since nothing costs 0 elixer, mirroring nothing should cost 1 elixer. Then if Mirror appears in your starting hand, you can just play it for 1 elixer and cycle to the next card.
Elixer Collector - The issue is that if you play the Elixer Collector behind the princess tower as your first play and the opponent doesn’t have the right cards in cycle, you can basically win the game. The root cause of the problem is that Elixer Collector doesn’t provide any defensive value. All other buildings provide some defensive value and, therefore, need to be placed in front of the princess towers in order to realize their full value. Since the Elixer Collector doesn’t provide any defensive value, it can be placed behind the princess tower and still realize its full value. The entire game of CR is based around the goal of damaging the princess towers. So when you’re forced to attack an Elixer Collector placed behind the princess tower, it basically changes the entire point of the game. That’s the real root of the problem. One solution is to give the Elixer Collector some defensive capabilities and reduce its elixer generation. For example, you could have it cost 5 elixer and generate 4 elixer. That way, if you place it behind the princess towers, you won’t get any value out of it. Then you just need to give it enough defensive capabilities to make it worth the investment.