She sounds just like my stepdaughter! I've discovered that some kids just HAVE to be the center of attention and are very self-focused. I've met several moms with similar kids (and they have other kids who are NOT like this) and I've now chalked it up to personality since these other moms haven't done anything differently with their other kids and are as exasperated as you and me!
My stepdaughter was like this from day one that I met her and is getting better. She is 9 now.
I've found that taking away things that have nothing to do with her behavior doesn't work. She's just bewildered because she hasn't made the connection that what she is doing is rude or wrong. She knows she did SOMETHING wrong, but doesn't "get it" even if it's explained. The consequence has to be immediate, but it doesn't have to be dramatic.
For example, if your daughter is moving off in the store and she won't stand where she's supposed to even with reminders then the consequence is she has to hold your hand. I guarantee she will hold your hand for a minute and then want to walk away, but now you explain why she can't. Also, while she's holding your hand you ignore her and go about your business. Holding hands isn't about being close. When she's really wanting to let go, then you explain what you expect and if she doesn't do it then you go back to holding her hand.
If she's bothering you while you're talking then you immediately let her know that she's interrupting, and that you are very disappointed in her lack of patience. If she's talking like a baby, then tell her you don't understand baby-talk and you'll be happy to converse when she's ready to act her age. You say it all matter-of-factly without getting excited (because she wants you to get excited) and you pay no more attention to it than you need to.
If she's going crazy, I do a time-out but I don't call it that. She sits in a chair until she is ready to act appropriately. I don't set a timer and make her sit for a period of time, she determines when she's ready. The chair is in the most boring part of the house I can find. My thought is, she doesn't have to play nice because I can't make her (you can't MAKE a child do something), but she isn't allowed to do anything else either.
I do make a point of heavily praising good behavior, and I often praise her good behavior in front of her to others. The funny thing is, the more I praise it, the more she does it. So if you can "catch" your daughter doing something right and heavily praise it, she will be more likely to do it in the future for the praise and attention.
Hope that helps a little! We're still working on it, and I feel we're headed in the right direction at least!