What Miss Whiskey said.
I have been there and done that and all was well.
I would put your hardware in some kind of bag, and put it in the tray. Spare batteries can be left in your carryon or in the tray.
DO NOT put batteries in your stored luggage! Against the rules so don't even think about it!
E-Liquids follow the same rule as any other liquids. Under 1 oz (a full 1 Oz bottle is like 29. somthing ml of E-Liquid) and put them in the same 1 quart baggie as your shampoo and other stuff.
Shampoo and other stuff is usually available in your hotel or motel room as well as anyone that you are staying with.
The last time I traveled with APV's and associated stuff, I had a Dovpo E-Mech, a Dovpo E-LVT and a custom made dual battery DNA 20 mod with me.
All of them had batteries installed and RBAs with liquid inside on two of them.
Being an experienced traveler, at the same time I was stripping down (AKA removing my boots, suspenders and cell phone......By the way All of my keys, change and stuff was already in a side compartment of my carryon bag) I made it a point (being diplomatic and stuff) of asking the nearest TSA agent if they had any problems with my vape gear.
She assured me that they (TSA) knew all about this "Stuff" and was quite nice about it.
But I did notice that she had a little "sidebar" with the other screeners.
And I went through in good order.
Except for one thing.
As I was going to another state, I also had my TomTom GPS and the "Sand Bag" dash mount thingy with me.
The "Thingy" got me pulled aside as it just showed up as a "suspicious" black mass on the scanners.
So they got out their special bomb sniffing stuff and gave it the once over twice.
Which was fine by me as while I was waiting for this to be done, I had my very own chair so I could get dressed again.
Sorry for the mini rant.
Just follow the rules, be nice and respectful and don't take a GPS "Thingie" with you and all will be well!
Back to the respectful part, as hard as it is to believe, the TSA screeners are people too.
Kind of anyway.
And think of all the ignorant assholes they have had to deal with before they get to your smiling face!
PS, don't even Think of bringing one of those mods with you that even looks like a hand grenade.
All bets are off at that point and we will see you in GITMO soon!