Toddler Behaviors

Spitting: A firm NO! Yuck! and a light tap/pop on the lips.

Running away, refusal to hold her hand: Don't chase. Just stand there and wait for her to return. She will. Especially if you don't go after her. She'll be shocked and wonder why you aren't following.

Going limp: Leave her there. Walk away and don't turn back. She's after your attention.

Shopping is boring for toddlers. Be sure to reward her with a trip to the playground afterwards!

I hate, hate, hate the dead weight thing.
I always think her arm will pop out of its socket when she drops.
I just started letting her go down, then telling her "byebye." When she realized I was leaving she immediately got up. Thats when I took her aside and told her we didn't act like that. She mostly does it when she doesn't want to leave a place.
Every now and then she still does it, but she's been getting better.
Good Luck!

Spitting - 'spitting is for outside and take her outside' - my son quickly lost interest in spitting since the physical move (not punitive, I would just go out with him) meant he had to stop whatever he was playing with.

Running away - sorry - she will outgrow it. Until then it's constant watching - some parents do use a leash - it's better than risking her run into traffic.

I have never done time outs for anything so I can't comment on the efficacy.