I'm really strongly against changing the type chart. That's something that's been the same since basically forever and changing it just means you have to have a copy of the new one as a reference at all times (or build one yourself as you figure it out I guess?) to be able to figure out what moves to use. And that's assuming you know what type you're going up against with all the new mons. With new mons AND a new chart you really just have to use moves at random until you figure out what's useful against a certain mon, and then you don't know why it's super effective for sure, especially if it's a dual type. Honestly the combination of those factors is why I stopped playing touhoumon before the second gym.
I agree with the swap of Destiny Bond and Shadow Punch, that's been changed. I'm debating switching Uproar for Rage.
The Uncarp line could probably do without Moonlight, now that I'm looking at it. I think it could be swapped for Mean Look, but it feels kind of odd to have two starters that can both stop escape/swapping. I swapped Bone Rush with Bone Club for a bit less damage (but I like a skeletal carp having a bone move). Horn Drill makes sense with the description of the final evolution (since it has a giant horn and all). Was your main issue with it a thematic one or a technical one? "yeah what?" doesn't really mean much.
Stockpile's weak in Gen 3, but Spit Up is surprisingly powerful (100/200/300 base damage for 1/2/3 stockpiles). I agree with Milk Drink obsoleting Swallow where it's at (swallow is 25%/50%/100% recovery) so I moved it down. It's kind of a thematic gimmick at this point. Switching out Sheer Cold for Blizzard works though.
The cute-weakling-turned-offensive-powerhouse unicorn family moveset:
Tackle 1
Odor Sleuth 1
Fake Tears 6
Sing 9
Absorb 12
Sweet Kiss 15
Horn Attack 18 18
Ingrain 21 22
Metal Claw 25 26
Metal Sound 29 30
Magical Leaf 33 34
Body Slam 37 38
Psybeam 40
Jump Kick 40
Leaf Blade 41 42 45
Steel Wing 45
Morning Sun 45 47 50
Moonlight 45 47 50
Solar Beam 49 52 55
Meteor Mash 49 52 55
Calm Mind 57 60
Swords Dance 53
Tail Glow 53
Screech 53 57 60
Psycho Boost 66
Superpower 66
It's a little harder to interpret because of the divergent evolutions, but yeah.
And yeah, assume evolutions' attack tables include the moves they could have learned if they evolved at the earliest level.
Edit: eeeeugh most of those moves are really powerful for the level. Oh well, maybe I'll rework it later or maybe its stats will make up for it. I'm going to go do other stuff for a while.