Morde can trade really well if you constantly keep up harrass with your E and at 6 if you have ignite/ult you can melt a squishy mid instantly, as long as you keep your shield (passive) full you'll never take any harrass but you will notice you lose health from spamming abilities, this is solved with hextech revolver. Anyhow, as soon as you notice your laning Partner is about half health Ult/Ignite and an E should kill them, A good morde is almost impossible to beat Have fun :D

Freezing the lane as mordekaiser is impossible you will be shoving the lane every wave, but you'll be getting every cs in the wave if you farm right. as soon as you have you hextech revolver and a few points in your E then farming is nothing and you can easily hit 100 cs at 11-12 minutes just q the line of caster minions and an e should clean them up, as for the melee minions you can wait for a last hit or Q-E again and it should clean them up if they were low from your wave of minions, if you are trying to sit back and not over extend because a lane is mia or you know the enemy jungle is near throw your W on a minion with full health and wait for a good time to E and clean up the wave.