My short answer is to stay calm, state your limit, and carry on as much as possible. (my cat deleted the other answer I had for you)
I wonder if the arguing is an attention-getting behavior, esp. the calling out after she's been placed in her room. I have had to learn to ignore a lot as a parent. When any arguing starts up, I simply tell my son "I've given you/explained my answer, and I'm done discussing it. So, we can move on and do X, or we'll need to take a break." Taking a break means one of us is going to leave the environment: either I will go away, up to my room, or if I'm doing housework, he will need to go to his room for a bit. Sometimes I leave because I am trying to show him that *I* can control my own actions and choices and make the choice to leave an unpleasant moment and that I can remove myself from the argument. It is a form of modeling, just like taking some 'cool down time' as an adult instead of banishing the child right off the bat.
Sometimes I will use a simple "I" statement and give a choice: "I am feeling very frustrated right now because you have asked me the same question four times and you won't accept my answer. At this point, you may either stop talking about this or you will need to go play somewhere else. Show me with your actions what you would like to do." (this implies, too, that I'll be watching/listening for him to move on and let the original question/idea go.)
Some of what you discuss is your daughter's fantasy/wish bumping heads with reality, and I think that when we see this sort of thing, it's good to name it and give a little empathy. "Oh, honey, I see... you really WISH that the computer would just send you those clothes, huh? It's a fun idea, but that's not how it really works. Bummer, huh?" or "I know, you wish you could have your hamster right now, it's hard to wait, isn't it?" Sometimes, those end questions touch on the empathy piece they need and help to move their brains/the conversation along to less arguing and to help them get in tough with their feelings. Further, it lets them know that we *do* understand that it is important to them.
As for flat-out backtalk, that only gets you one warning ("You are using a rude voice and I do not appreciate it. Try that again or wait until you can be polite, please." ) Usually, this is a bid for attention, so I try not to give it too much of a reaction, just "I don't want to be around you when you are being rude to me. You may play in your room until X." or once again, I'll go take a break somewhere else if that's an option.
One thing to keep in mind: we adults forget that sometimes, people who live together aren't always nice to each other. It doesn't mean it has to be the norm, just that we are all human. So when I get crabby with my son or husband, I am sure to apologize and let them know I made a mistake and it wasn't right of me to grump at them. Being aware of one's own actions is important in helping our little ones be aware of their actions, too.
ETA: One important thing to add is this: if you think the behavior comes from her desire to get your attention, be sure you are giving her lots of that at more appropriate times. One practice I use when I start to see attention-getting behavior is to give lots of nonverbal, loving attention during times when my son is busy doing things which he enjoys. For example, if he's busy playing with Legos, that's the time I'll go and kiss his head, tousle his hair, rub his back, give his shoulder a friendly squeeze.This is an expression of our love for them when they are not doing anything to please us, necessarily, but that we love them for WHO they are, just for being. This is a profound and powerful progressive action to take and does really fill them up more than talking or praising good behavior will. Being loved just for being yourself... If I'm not in a loving space, I might also use some craft sticks and move them from one cup to another (apron with two pockets, same thing)... this reminds me that he needs a lot of this during some times and helps me keep track. Shoot for 20 of those 'positive strokes' a day (no, I'm not joking, this intensity DOES make a difference.... I've seen it work a lot) when you are seeing annoying, attention-getting behaviors. It will get better!