A coupla questions concerning this adjacency businees with Poison Ivy. Would she be able to use Willpower if Thomas Wayne was adjacent to a plant object?
INSPIRATION: Adjacent friendly characters can use Willpower.

Also, for purposes of this feat:
Infiltrate
Prerequisites: Stealth or Shape Change
Choose a character.

This character can ignore other characters for movement purposes, but must end it's movement adjacent to an opposing character.

Would she be able to end her move wherever she wants so long as an opposing character somewhere is adjacent to a plant object?

Oh and one more thing, when she "teleports" thru her objects: she would not have to walk up to one plant, jump to another, and then continue her move, right? She would simply at any point during her move whether there's an plant beside her or not, jump to a square beside a plant and keep moving, right?

Sorry, I 've got another question in regards to carrying. Could Poison Ivy be carried by any friendly character adjacent to a plant?

"When moving as a result of being given an action, this character may carry one friendly character...
To be carried, the friendly character must be adjacent to this character at the beginning of this character’s action."

Thank you for the recap. Very clear. Rep to you!

Right. the issue is the rule that says you can't use a game effect if you already have that game effect, basically. It not being printed on the dial isn't the thing that gets you around it, it's that she doesn't have Incap until she is given an action to choose that option: the same would apply to Nico. If her power simply said "Ivy can do A, B and use Incap" she would be prevented from using Batarangs.

In fact, if you equip her with Batarangs she can't use Entanglements.

Dang, for real? I totally understand why, but dang, for real?

Is that right?

Batarangs
Give this character a ranged combat action to use Incapcitate to target all opposing characters within 6 squares and line of fire; this character can use "Improved Targeting: Ignores Characters" for this attack. You may give this character an additional action token and if you do, hit characters are given an additional action token.

The resource doesn't actually say it gives the user Incap. It says to give the user a RCA to use Incap. Is 'give the user a Y action to use X' the same as 'user has/possesses/can use X'?

No, you're right: I was thinking of the relic version:
Character can use Incapacitate, the Sharpshooter ability and possesses one additional "target".

I would say between the resource version and Entanglements you have a choice, and it can change throughout the game as in both cases you'd need to give her an action to have access to the power.