when I try to participate in team fight I just end up getting focused
on an then dieing. The irony is that when I'm not focused on it still
feels like I'm barely participating.
Morde's passive Iron Man turns damage from abilities into a shield that protects him. Always try to charge the shield on minions, jungle creeps, etc before a team-fight. Morde is surprisingly squishy without his shield up.
If your shield is down and a teamfight breaks out, stay on the edge and launch your abilities into the crowd. Target their carries if you can reach them, and give your Creeping Death buff to the tank/bruiser/initiator.
How close should I be to the fight?
Close enough to hit with your abilities. Since Morde is constantly regenerating his shield while he's doing damage, he can take a surprisingly large amount of damage.
Should I be trying to auto attack the other champs?
Only auto attack to trigger Mace of Spades.
Should I only be worried about getting my ult off on their squishies--ignoring all else?
No, because if you die, your ghost dies too. Your goal in any teamfight is to use your ultimate on their ranged carry. Because the ghost can only auto attack, champions with high attack speed and AD make the best ghosts.
Or, should I ignore the fight and just be pushing another lane?
Morde's greatest strength is turning a 5v5 into a 6v4 with his ult. While Morde can clear minion waves very quickly, he lacks the AD damage to destroy turrets as fast. It's generally best to be in the teamfight, but every game is different; sometimes it's better to push, so this comes down to a judgement call.