Newb to PoE. Making Shadow Mage.

Well, I started about last saturday. Today, I decided to make a Shadow, and instead of going bows/melee with a combo of magic, I'm going pure magic.

Anybody have any advice on how I should build my character? Screenshot of what I have so far below.

You are going to need more knowledge than what can efficiently be condensed on these forums.
As such, I'd say, play as far as you can until the 23'rd October where you'll get a free passives reset, likely a onetime chance.After that you likely will be able to choose a spell to specialize in and study a few guides.
Going cold you'd might want to try out a clarity aura and a 4-link of Freezing pulse + faster projectiles / mana leech + lesser multiple projectiles + faster cast. (only a linked manaleech gem will allow spells to leech mana, you can't get that from gear or passives, yet.)

This isn't the most powerful set of passives, but it does underline the fact that you will want a lot of mana and fast cast if you want to spam Freezing pulse or ice spear.