The Rainbow color card only contain scry card, is that bug? I can gain other Rainbow cards through chest, but can't gain it from snecko.

I'm not even finding the rainbow cards, probably because of the mimic mod I have, but even when it isn't a mimic the card still doesn't show

the character skin dosn't seem to work for me; I've seen it work in your screenshots and in frost-prime's video on the mod, but for me there is literally no skin at all, even when limiting the mods to just basemod, stslib, and rainbow.

presumably the issue is the one mentioned in the mod launcher:
This mod explicitly supports StS 12-22-2020.
You are running StS 12-18-2022.
You may encounter problems running it.

but other than the skin not working, everything else about the mod seems to work in my game version

It seems the starter relics are added to the end of the list after selecting the number of characters. That causes some issues with mods that add additional "starter" relics used for tracking mechanics (e.g. Evolution), as Neow rewards will then swap out those additional relics instead.

have a null pointer exception that's causing the game to fail to start

Exception in thread "LWJGL Application" java.lang.NullPointerException
at rainbowMod.ui.RainbowCharSelectPanel.makeCharNum(RainbowCharSelectPanel.java:53)
at rainbowMod.ui.RainbowCharSelectPanel.<init>(RainbowCharSelectPanel.java:35)
at rainbowMod.RainbowMod.receivePostInitialize(RainbowMod.java:213)
at basemod.BaseMod.publishPostInitialize(BaseMod.java:2300)
at basemod.patches.com.megacrit.cardcrawl.core.CardCrawlGame.PostInitializeHook.Postfix(PostInitializeHook.java:9)
at com.megacrit.cardcrawl.core.CardCrawlGame.create(CardCrawlGame.java:307)
at com.badlogic.gdx.backends.lwjgl.LwjglApplication.mainLoop(LwjglApplication.java:149)
at com.badlogic.gdx.backends.lwjgl.LwjglApplication$1.run(LwjglApplication.java:126)

If you haven't unlocked a character for one reason or another, they still get added to the pool of options, and you cant turn them off since you cant select them in the character selection menu.

If possible, adding a config and delegating the turn-on/off to that would probably be sensible.