Hey yall, trying to iron out some things for a team I'm building.

My question is with Kobik's Special Trait. Would this allow me to include a character on my sideline to use in conjunction with this trait? The reason why I ask is I remember sometime back there was a ruling where you just can't use random things on your sideline or maybe I'm losing my mind.

All I can find in the Rulebook currently is on Pg. 3
Would I be correct in that Kobik's trait in questions falls in line with Sorry if this was a little wordy, but want to dot my I's and cross my T's before hand and not look like a fool.

Yes. Kobik's trait allows you to add a character to your sideline that would qualify for her trait.

If you have a figure with a object, like a gem, and when I use Kobik's "Rewrite History" to replace the figure, does the object transfer to the newly replaced figure?

No. 2018 Rule Book, page 31-32 (note the bold text):

Thanks for the reply.

Is there any point restriction on the sidelined replacement character?

Yes. The point value of the character it would replace.

That's good to know because I like to run The Zombie (Simon Garth) who comes with a Relic token that allows people to control him, opposing players are granted Mind Control to control the character if they pick up the relic token. But, if a friendly character picks up the token then it's a FREE action to command The Zombie to be given ANY ACTION because it's not "mind control" for the friendly character.