I am having a hard time surviving in this game with light armour, one handed mace, one hand conjuration. Should I equip a shield when I am in close combat?

If you're using conjuration, you shouldn't be having much trouble surviving. Regardless of your armor. Cast your spell in front of you when battle starts instead of trailing it behind after you.

That said, there's no point in one-handing conjuration either. Unless you're using a bound weapon with it. Atronachs are strictly fire and forget.

I am assuming that using one hand for a fire spell weakens the damage?

One hand gives you the base damage, two gives you double the damage (as you'd expect, you're casting the same spell twice simultaneously), and two with the dual casting perk gives you 2.2x the damage (but at 2.8x the cost, iirc).

Traditionally, a summoner Mage will conjure a creature and do ranged damage while the pet tanks. If you want to go toe-to-toe you'll need several Light Armor perks or at least a shield with the Quick Reflexes perk.

light armor is hard way to go untill you get your smithing up there, and get some skill points in the lght armor, best bet early on, Bow and run with con creatures or zombies backing you up
once you get to glass on smithing then it becomes viable and the perks to add bonus for like armor and all light armor, then its just as good as heavy armor! but still watch your health, when they fix the rest. for the 360 i will be back to being a god with my fire lighting cold rest's. with light armor spells kill quick take out the spell casters fast. and sneak sneak sneak, always enchant muffle on your boots no matter what that way you can just run behind cover go to sneak and kill off things while you are retreating untill you are hidden again. any time i crawl im in sneak even after they spot me that way i limit the peps that know im there to the fools in front of me. hope that helps

Thank you for all of the suggestions!