I think that most of them go through the bedtime phase. Do you have a bedtime routine? Establishing one even a short one could really help, especially if you do something like read a story to her in bed. We talk about all the good things that happened that day, and get DS to tell us what he wants to pray about (trying to encourage him to think about things he is glad about). Also we always end off telling him that he is the most special boy in the world and we are the luckiest parents in the world to have him as our son, and that we love him lots.
Also, it really helped when I showed him the clock (he is 2.2yo) and showed him the number for the hour. He goes to bed really late as we are late risers. So now he knows 9pm is bedtime (and he can recognise the 9). We made a big deal of saying, "let's go check the time". "what time is it? 9 O'clock. What does that mean?" - then he would say "9 o Clock bedtime!" It really helped him to understand that at a certain time it was time for bed. Lots of positive reinforcement, telling him what a big boy he is going to bed so well.
Gradual withdrawal did not work for me. When he started crying when I left the room I eventually told him he could cry if he wanted but I was not coming back. He cried for two nights, and then realised I was serious. Now if he really needs something he calls and tells me what he needs.
I agree with the other comments about tackling one thing at a time. I don't see the high chair thing as a big deal. She'll grow out of it when she is ready (it might be a bit of security for her right now).
As for potty training, this can be tough, and I wouldn't push it at the moment given that she has the seperation to deal with. I bought a great kids book which showed pictures of little kids selecting a potty, and pulling down pants, then sitting on the potty. It was a fun colourful book, and showed that the little kids wear nappies and the bigger kids use the potty, and even bigger kids use the toilet. My DS loved looking at this book. I also got him to sit on the potty just a couple of times a day (usually before bathtime and after afternoon nap). After a while he bagan ASKING for the potty. In the meantime, just let her see you go to the loo. When she is interested do lots of positive rewards (eg stickers or some other small fun things). Sounds to me (when she talks of being too little, and being worried about falling in, that she's just feeling a bit insecure right now and needs some TLC and does not want to face any other big changes).
Reward positive behaviour. She probably needs even more encouragement at the moment, and is probably feeling a bit insecure.
However, the behaviour in the supermarket is really something that I would tackle if I were you. That would be too stressful for me to allow to continue. All kids test the boundaries, and yours is pushing and pushing and not finding any boundary! Kids actually find boundaries comforting (although they usually only admit it in later years), there is some security in knowing that mum cares enough to make sure I do the right thing. Your daughter behaves like she does in the shop because she can.
Explain to your DD that you are now going to have new rules for shopping. If you can, try doing shopping without her (or do the internet shopping), and tell her that you'll take her shopping again when she can behave like a "big girl". We had a problem with DS wanting to run around in the shop at 2y.o (thanks to MIL allowing him to do that). He yelled to get out of the trolley. I explained that if he wanted to go shopping with mummy he had to stay in the trolley (I can't manage the shoping and a buggy and him at the same time, and I will not allow him to run around - it is not fair to other shoppers, and there is always the odd chance of someone abducting him while he disappears around a corner. The risk is tiny but not one I am prepared to take). He threw a fit and wanted to run around. I told him that if he did not behave we would go home and he continued to yell to get out. I told him that he had a choice - he could either stay in the trolley and shop with me, or we could go home (I find giving them choices really empowers them, because then it is their decision). He persisted so, I took my full trolley to the service counter and explained to the (amazing) woman there that my boy was not behaving properly and so I had to take him home until he learned how to behave like a big boy, so could she deal with my full trolley. DS was FURIOUS. I let him yell. When he calmed down on the way home, I explained to him that I will not accept that behaviour in the supermarket, and even if granny thinks it is ok, we do not behave like that with mummy. I explained that he is a great boy and I love him very much, but I was not going to have him yelling at me in the supermarket. I also explained that I would not be taking him shopping again until he could behave like a "big boy". He begged to go back, said he would be good. I took him back on another day, and he is an ABSOLUTE ANGEL in the shops now (he is now 2.2yo). I give him fun things to look at while in the trolley, or ask him to point to things he thinks we need to put in the trolley. If the item is non-breakable, I give it to him, and he throws it in the back. Or I give him an item to look at (like a bag of rice) and tell me what colours are on it, or what he thinks it is, what it is for, how do we cook it etc. (all this makes him feel involved). Of course he gets ratty when he is tired, so I try to avoid taking him shopping when he is tired. But he knows that he needs to behave. He also knows that I will not hesitate to take him home again if he does not behave. Occassionally I do let him get out of the trolley and he would not dream of running around. If he pushes the boudaries I ask him "do you want to go shopping, or do you want to go home. You choose. If you want to shop, you need to (stay in the trolley and with a big smile or hold mummies hand)". Occassionally he says he'd rather go home, and then we do (and try shopping another day). Mostly shopping together has become a pleasure.