I like your ideas and I would welcome this "mechanic" in the game. This is mainly because how your cards require you to build your deck more differently and you have to have a specific set-up, in order to get the big rewards:
1) Archmage's apprentice - holding onto a 1-, 2- and a 3-mana spell by turn 10 and then casting all of them (with your 4-mana mage) at the same time.
2) Prince Nazjak - this reminds me of Defile in the terms of having a specific board state. However I think, that this is the weakest in comparison to your other ideas - a) kinda hard to execute imho (if your opponent is familiar with your deck strategy, they will try to counter it), b) not to mention, that 5-mana cards have to be really rewarding (+ reliable), in order to be worth the inclusion in an aggro deck. I would suggest to boost the buff a bit - his effect should set the stats of your minions to 6/6, which also goes in line of what you are trying to design. Inb4 kudos for the prince theme.
3) Medivh, the Mastermind - my favourite card from all of your ideas. So I like how the requirements are hard to fulfill (surviving by turn 10+, playing really expensive minions, spending 10 mana for an 8/8 body and not answering your opponent's board state and then 10 mana again for the reward itself), but the reward is really powerful and worth all your efforts. I think, that there would be a competitive control deck running this card, not to mention, that tons of casual ones will form just for the sake of it.