Welcome to the wonderful world of toddlerhood!
A couple things come to mind. One is those pesky molars. I think we went through a week of hell for 1-yr molars with my son. He was miserable, woke up at night, etc.
Also, for sleep disturbances in a kid who normally sleeps all night, you would want to rule out an ear infection.
If you're sure those aren't the case, it would appear that you simply have a regular toddler on your hands. It doesn't mean she'll grow up to be a bad kid or disrespectful. This is just where she's at developmentally.
Using the crib for "time out" isn't a bad idea. It will not cause the crib to be associated with something negative, etc. Time out isn't a punishment in and of itself, it's exactly what it is -- time to chill out and recollect herself. The reason you use the crib is because it's a safe place for you to put her so that you can walk away.
You can use love and logic with her, it's just that you will be repeating the same consequences over and over and over because it will be her job to test and test and test boundaries. As long as the boundaries stay firm (I have a screaming fit, I go to the playpen where I can't see mommy; I throw my cup, I don't get any more juice; etc.), she'll give it up after a couple weeks (yes, a couple weeks...or more) and pick a new area to test.
The love and logic concept that I used a lot when mine were younger was "If you can't change the behavior, change the location." If the fits and whining are non stop, I would say, "I sounds like you need a little break. It's time to go to your room." Then I'd deposit the child in his/her crib and either set a timer or do some sort of chore for about 10 minutes. I made sure that I was out of eyesight and earshot. Ten minutes always worked well (still does with my 2 yr old). It gave them time to calm down and start entertaining themselves with crib toys.
Just know that having some consequences and tools to respond to the whining and tantrums doesn't mean there won't be any tantrums. It just means that you know how to handle what comes at you! You're in for tantrums for the next 4 years!
As far as sleeping, if there's nothing that she needs and she's not sick, if she gets up in the middle of the night, it's fine to go check on her, but pat her on the back, hug her and say goodnight. You may have to listen to some screaming for a night or two, but she'll figure it out.
Good luck!