If an Order of Scribes Wizard took, for example, both burning hands and false life, could they use False Life Hands (exchanging fire damage for Temp Hp) on their allies to give temp hp as a sort of damage type? It would be cool but I can also accept that temp hp isn't particularly a damage type so I could live without that, even if it's very cool...

A few other questions to follow as well,

Acid stream + change in damage type (force, thunder, etc), as well as other DoT concentration-spells, how would you rule that? I'd love to see cloudkill with something other than poison!

Chromatic orb's multiple damage types, can a wizard use them all on every spell if he knows Chromatic orb?

Catapult and other spells deal bludgeoning damage, and there are others that deal piercing/slashing damage; can my other spells deal these types too or not? (because they're physical damage types sorta)

Can I choose, in the case of multiple target spells (scorching ray, magic missile, ect) a damage type for each individual attack roll, or must every roll deal these types of damage?

Can my prismatic sprays (if I ever get to that level) be all one type of damage? Maybe not the status effects, although changing the status effects of effect spells would be cool too (if not OP) 

If you think of any cool uses for the feature let me know in your replies as well!

Damage is anything listed under Damage Types or specifically described as damage; healing and temporary hit points are their own thing, and they're balanced very differently from damage (Cure Wounds heals less than the average damage spell inflicts, for example).

As far as the Awakened Spellbook feature is worded, it seems that if any of your spells is capable of producing any of these damage types, then you can choose that as the damage type whenever you cast a spell using a spell slot; the last part there is important as it seem it won't work on cantrips, or anything cast without a slot (like Spell Mastery and Signature Spells).

Regarding how good the sub-class is; personally I think it seems okay. Being able to choose damage type on any spell is a very powerful ability as it means you can throw out more force damage than normal (which few things are resistant to). If you know what damage and/or saves a creature is weakest against you can effectively build a custom spell to use against that enemy by choosing the damage that will hurt the most, on a save or effect that will make the biggest impact. While it might be less exciting for regular enemies, it can make a huge difference against tougher ones with their various resistances etc.

You're also gaining half cost spell scribing on all spells, not just those from one particular school of magic; this might not be a big deal depending upon your campaign, but if your DM requires you to handle this properly and your resources are tight then it will make a difference.

Master Scrivener is neat; a free upcast 1st or 2nd level spell as a scroll per long rest is nothing to sniff at.

Manifest Mind is really interesting, though that's not till 10th level so I do wonder if it's coming in a bit late (should be the 6th level ability?) as being able to summon a spell turret is a pretty big deal, even if it's not super tough, especially if you consider how it might interact with Leomund's Tiny Hut or Globe of Invulnerability for example.

One With the Word is interesting; the teleport ability is neat, and the free resurrection is something you would hope to never use, but if you need to, well, why not?

I think overall it's okay, I'd rather get the turret ability earlier even if it were limited in some way (e.g- max 2nd level spells) as it feels like 10th is a bit late for that, but yeah, it's a neat sub-class.