J.M.
I would not accept the way that she is behaving with you. She should not scream or yell at you. You need to talk with her that she should not be treating you this way. At 4 years, she should understand that it is not okay to treat mom this way. It almost sounds like she wants to be in control at times. The other question is how much sleep or rest does she get each night? If she is not well rested she could be displaying some of this from being overtired.
When it comes to conversation, you may need to pay alittle more attention and offer a sentence or two and then ask her a question. It will offer her a chance then to let her tell you something if she wants.
When it comes to you looking at her and she screams and cries, I would not accept this behavior. You are the mom and she needs to just deal with it. If she says "dont look at me" then send her to her bedroom and let her know that when she is ready to come out and apologize to you then she can come out. This could though be a time when she is overtired too.
The time-out behavior is not unusally but also not acceptable. I am not sure how long you have been using time-out with her. If it is recent that I am not surprised if she is lashing out. My 2year would be upset, cry and try to hit me because he did not want to go in time- out. At 3 years though, all I have to do is mention time-out and he usually stops misbehaving on occasion though he stills needs to go in time out and he will attempt to climb over the chair and hide.
If you have been doing time out for more than a year than I would go back to the basics and get a chair, stair or mat for her to sit in during time out. Every time she gets up, starts screaming, crying or hitting scratching, just keep returning her back to the time out chair and make her sit for 3minutes. do not say anything to her after the first time that you explained why she is going in time out. She is 4years and she could go with 4min but I would start gradual. For my 2year old, I started with 30 sec, 1 min, 2min, 3min and now when he will sit until he is calmed down and then will get out by himself becuase he has developed to know when he is ready to get back to whatever he was doing before.
good luck