Should I always be drawing a card when I untap key to the city ?
Always, no, but usually. Even when you've got something like a Bloodhall Priest that wants your hand to be empty, Key lets you turn around and discard one of the two things you drew while you presumably cast the other one. It doesn't always work out, but the percentage is very high. Plus, it doesn't take long for an unblockable 4/4 to win the game even if you're not getting the trigger.
Key to the City serves a bunch of purposes in the deck and netting card advantage is only one of them. Sometimes you just need to punch a Scrounger through a couple times to win. Sometimes you need to deal three off your Unlicensed Disintegration. Sometimes you need to work through a land flood, or even go the other way; I've had games where I played Key on turn 2 and immediately pitched something like Pia and Kiran, then paid the two, just to try to get lands to apply the rest of my hand to the board. Mostly, Key is a cost reducer for the 20% of your deck that is madness cards, and then lets you recoup the card the next turn, hopefully finding another Temper or Alms to keep the cycle going. It doesn't take much to end the game this way.
I definitely do not advise adding more lands. Mulligans exist for when you get 0-1 in your opener (though some hands that are thick with Nerd Apes and Couriers can keep a one Mountain hand and give it a try). Two lands turns on most of your deck and is usually all you need to justify a keep. Neonate, Copter, Key, and even Sanitarium can all help filter your deck to deal with mana floods and mana droughts.
As for Fiery Temper to their face or not, it all depends on game state. The way to play the deck is always watching their life total. Sometimes you will only need to deal 6-8 points in combat to know that you have the rest of the damage in your hand. Usually, though, you will want to Temper to clear early blockers or threats (Sylvan Advocate, Tireless Tracker, opposing Copters) so you can keep swinging, with any Tempers drawn late being held onto for finishing purposes.