The Renegades are marked as (Neutral) in the rule book, how do those fit into the game when using the other six factions? I understand in the starter set for them you can use them for a 1v1, but in a regular 3v3 hero game can you put them into other codexes?
For example, when using the Blood Anarchs(Red), could you use two of the red specs and then one of the neutral specs?
Along those lines, are you allowed to add Green cards to your red codex too? If so, how do rules around this work?
Yes, you can put the neutral heroes into your team of 3 heroes in a 3v3 hero game. You can combine any three heroes you want, actually!
For each hero you choose for your Codex, you must put all of that hero’s cards into your codex, too. So if you choose Bashing/Blood/Fire, you will have all of the Bashing, Blood, and Fire cards, and none of the Anarchy cards in your Codex (and so you won’t be able to play any Anarchy cards).
If your three heroes are all the same color or neutral, your codex is “monocolor”. If at least one hero is a different color, then your codex is “multicolor” and you must pay 1 extra gold for the first tech building or add-on you build each game. So if your team is Anarchy/Blood/Growth, that has Red and Green heroes in it, so you must pay the penalty.
Any Red hero can cast any of the Red or Neutral starting deck spells (also called “minor spells”) normally. Same for Green heroes casting the Green and Neutral starter deck spells, etc. But if a Green hero wants to cast Red minor spells, it costs 1 gold extra. Same if a Neutral hero wants to cast a Red or Green minor spell.
Also, only a spec’s hero can cast that spec’s spells. So only Troq can cast Bashing spells, only Zane can cast Anarchy spells, etc. This is different from the minor spells just costing 1 extra, above.
That should cover it! 
Complete rules for 3v3 heroes are here, starting on page 10: Dropbox - codex_rulebook_46.pdf - Simplify your life
Note that you don’t have to pay the 1 extra gold for your first tech building/add-on if your only multi-color is a neutral spec. So a Fire/Blood/Bashing deck would not have to pay the penalty.
So to summarize:
If your deck has at least two different colors (red/green/black/white/blue/purple), you have to pay an extra gold for your first tech building/add-on. Any of your heroes can play minor spells (the ones in your starter set), but they have to pay an extra gold to do so if they are of a different color.
The neutral specs are “colorless”. That means they don’t count as a different color for purposes of whether you need to pay extra for that first tech building/add-on. It also means that if you are using the neutral starter, any hero can cast those neutral minor spells without penalty.
Cool, thanks for the explanation! This cleared up a lot.
Note that, as far as I can tell, if you were to play something like Bashing / Blood / Fire with the RED starter, River would have to pay an extra gold to cast any of the Red starter spells.
Yes, Troq and River do have to pay the extra gold to play non-neutral minor spells.