My first two were like yours, easy, not demanding, never a tantrum, not making messes everywhere.
Number 3 comes along and WOW! She's a whole different bird. I had to pull out the patience card and I use it all day every day. Oh - and the creative card too.
I think the demanding and whining are normal for a 2 1/2 year old as they are trying to figure out their world and their place in it. (And how to push your buttons!!!) She is trying to find her limits with you. This is the time that you use to teach teach teach!
No more demands - correct her EVERY TIME she demands something (mine does this too - "Mommy I want a snack NOW"). I have no idea where she got that from, since my other two never do that. So I gently say "Barbie, please ask nicely - May I please have a snack Mommy". And she gently repeats "May I pwease have a snack Mommy?". Do it every time she asks in the demanding voice and eventually she'll surprise you and just do it herself. You said you make her say please and thank you, so just keep doing it. Eventually she'll get it.
Mine tantrums too if she doesn't get what she wants. Screaming, crying, etc. This is where the creative card comes in. It depends on the situation, but typically I can distract her with something else. It doesn't always work, so I tell her she cannot have that and I let her just cry until she realizes she's not getting it.
I don't know if time outs will work the way you want them to on a 2 1/2 year old. They are still a bit too young to understand the concept and I really believe redirecting/teaching is better at that age. I would only use them if she is hitting or doing something harmful. And some kids don't respond to time outs at all. You have to figure out what works for your child. They are all different and what worked for the first two may not work for #3.
And believe me - it drives me crazy too, but before you know it she will be a teenager and you'll have a whole new set of issues. Enjoy that little sweetness while you can and make sure you get some mommy time without kids once in a while. Soooo important when you have a toddler!
ADDED: i just have to add - this morning she came into the kitchen and said "May I pwease watch Nemo Mommy"? Oh - soooo cute. I praised her for asking so nicely and now she's watching Nemo nicely.
She really is getting it!!!