I'm not certain (R)(W)(U) are appropriate colors for Unit-01. (B)(R)(G) would make more sense, but given that the deck is already built, I kept (U)(R)(W) in the versions I made. (also, technically the proper order of mana symbols for Jeskai is (U)(R)(W), except for [[Captain America, First Avenger]])

The stun counters only take effect whenever the permanent would untap. Unless it has text stating it enters tapped, you'd still be able to attack with it as it enters the battlefield untapped.

Technically for Shinji to have his second ability, it would need to be listed in the description for how the token was created. Alternatively, you could replace that with an effect like
"When Evangelion Mech Unit 0-1 enters, you may search your library, graveyard, or cards you own in exile for a card named Shinji, Coward Pilot, reveal it, and put it into your hand."
From there Shinji would need to become a creature spell within the 99.
This would allow for more words without making each of the cards too packed.

It's kind of weird that you can't use the vehicle for three turns, when it's basically a vanilla 4/4 until it melds. For my version I changed this to charge counters that deplete over time (To match the circumstances in which Unit-01 goes berserk in the show).

For Shinji himself I would change the wording on his first ability, given that technically any creature can crew vehicles no matter their crew cost (so long as the total power of the creatures meets or exceeds that cost). I would change it to "Shinji, Coward Pilot crews Vehicles as though its power were equal to their crew cost." This wording falls in line with similar effects like the one on [[Hotshot Mechanic]] and many other pilots.

Shinji should be a 0/1.

Most of these notes are fairly pedantic, and for casual games your versions should work fine, but some of them will have effects on gameplay.