Overall, this is a very mixed bag, with some good ideas, a nice layout, but a power balance that's all over the place.
I'll do a spell-by-spell review here:
Accursed Smite: Seems too powerful for a alevel 4 spell. At level 5, it would probably be more fitting though.
Bee Sting: This is fine, I like it and it seems nicely balanced for a level 1 spell.
Celestial Armoury: Incredibly underpowered for a 5th level spell. The concept is good but it's basically an alternative Witchbolt, which is a Level 1 spell. This would be fine at Level 1.
Unless it's meant to do a LOT more?
Conjure Trap: Seems fine overall. You might even get away with it being castable as a ritual.
Conjure Venom: Also fine.
Dimensional Rend: This has no right being a level 3 spell.
You get to attack every creature within a 40ft cube (anyhting from 1 to 60 creatures), doing 8D6 magical damage on a hit, half on a fail, then basically teleport anywhere within 25-35ft.
Other third level attack spells do things like... +3D8 damage to an attack, or creatues within 5ft of a point take 3D10 damage on a failed dex save, or variants of 1D4 to 3D6 extra damage to a strike.
Even Fireball, one of the more powerful level 3 spells is 8D6 fire in a 40ft sphere on a failed Dex save.
Rend has a roughly 25% larger area, deals magical damage, is more likely to deal full damage AND lets you teleport after.
As a 'high' 4th, (or even 5th) level spell, this would be fine, but not as a third.
It's also unclear if you roll damage seperately for each creature (as it's a roll-to-hit-each, which implies it is), or if it's a flat one-roll-for-all, like area spells.
This is doubly confusing, when things like Celestial Armoury you have as a 5th level spell, or Doffing Smite at 4th level.
If the spell level was 4, or the damage reduced to say.. 4D6-6D6, it may be fine as 3rd level.
Doffing Smite: This is mostly fine, if a little weak. It's definately a low level 4, or a higher level 3 spell. Also, it would benefit from 'less than half health' rather than 'less than 40'.
Explosive Strength: This is basically an upscaled Thunderwave / Fireball+. It's certainly an upper 3rd level spell. I think drop it to 6D6 and it'll be perfectly fine.
Better average + total possible damage than a level 3 Thunderwave, better knockback, slightly less damage than Fireball.
Herculean Force: This I reckon, should be a first. I'd even say make it +1 minute, +5ft throw for each level higher used.
Lingering Shadow: This is a very interesting, and honestly well put together spell. Fine as is.
Purifying Strike: This is fine.
Winters Bite: Also fine.
At the end of the day, this document is a bit of a roller coaster, and has a lot of good ideas in it, that I want to include, but some of it just makes myself, and my group confused.