These are all interpersonal problems rather than gaming ones. Here's how I'd handle each of them.
Same Character I'd tolerate it. Not a big fan of this kind of behavior, but it happens. I think it's a roleplaying maturity thing.
One thing I used last game might help you. I like the list of 100 questions about your character, but didn't want to overwhelm my players with homework. Instead of asking them to fill out the list I asked them all 1 question from it before each game. This worked great because it helped grow their characters as the game progressed and because it was one question at a time they actually put thought into the answers.
I bring this up because some of the questions were useful tools to differentiate the player from the character. Asking them what advice the player would give the character, how the player and character would disagree, etc, was useful for the players who were a little too close to their characters. You could ask everyone this like I did or even ask her alone.
Setting inappropriate powers I'd brainstorm with her. "No, you can't play a robot because they don't exist in the Forgotten Realms. How would you feel about a golem?"
I think the important thing here is to work with her rather than restrict her. The idea isn't to keep her from playing a robot. It's to figure out what she is trying to express by playing a robot and then figure out a setting appropriate way to express the same thing.
Since you are the party who knows the most about both the restrictions and features of a campaign setting, you're in a better position to figure out alternatives to her ideas than she is.
I also find it helpful to use book and movie examples as a good way to communicate the feel of the game you're going for. I was trying to run a gritty and dark campaign, but one of my players wrote a 5 page faery tale for her background. With her permission I altered it, but it was clear that she wanted to play a G/PG character in my R rated game. Neither of us were happy.
Since then I've told my players what books or movies inspired the game I'm planning on running. This doesn't have a perfect success rate, because some players won't read books, but it's drastically cut down the number of mismatched characters I received. If only the Game of Thrones TV show came out before I ran my GoT game, the players might not have tried to act like an adventuring party.
Finally, it is possible that a character can't be fulfilled in a certain setting or even a certain campaign. As GM you need to recognize when this is the case. In this case I'd suggest having the player shelve that character until the next game.
Multitasking Intolerable. It's one thing if she's off screen for a while, but if she's playing she should play. If she doesn't have time for the game or if she isn't interested enough to play 100% of the time, she shouldn't be there.
This is one case where I wouldn't go for the one on one conversation. It would seem like you're bullying her. I'd lay down the law in front of everyone so that it's obvious the same rules apply to everyone.
For how to approach the situation, I think it depends on what kind of multitasking the player is doing. I'm willing to be less than polite to someone who is playing video games at my table. For homework, I'd ask nicely. Homework is an obligation, video games aren't. I'd also offer that the player could skip the game session.
Sometimes players feel like game sessions are an obligation too. I had one player with anxiety issues who was getting stressed out about game, but didn't want to miss hanging out with people. The answer for him was to invite him to come hang out while we game, but have no character of his own. I let him play NPCs when he was up for it. If your player is stressed to attend session and finish homework, try telling her she can stay at the table but not play while she's doing her homework and then when she finishes she can come back in. Tell her that it's not that you don't trust her to handle both, but that it's distracting for everyone else.
Also, to clarify when I say multitasking is intolerable, I mean playing RPGs and doing something else entirely. If you're playing game and looking up spells for your next level or writing your backstory, that's fine by me. Your head is still in game mode. Depending on the game, I might even allow miniature painting, but that's pushing it. (The sort of game where I've seen that done in a reasonable way is 3.5 with long combats. When it's 30+ minutes between turns, putting another shade of red on your cloak is entirely reasonable.)