She's only a puppy and will make occassional mistakes! I would go read a sticky thread on potty training on Training Forum. I used it myself to train my puppy! Also, at that age, she probably needs to go out pretty frequently. Try not to give her any chance to make an accident in the house.
With the barking, you just need her to bark it out. Don't give her any attention, not even a "no!" You are on the right track by letting her out only when she's been quiet. This will teach her that barking won't get her out the crate. Did you try introducing the crate to her first? First, letting her explore it, sniffing, and what not. Then, put some enjoyable treats in there for her to find. Each time she goes close or in it, praise her like crazy. Eventually, she'll love her crate because she associates it with good feelings/treats. When you first leave her in there, don't let it be any longer than 30 minutes. Then you can increase the amount of time away. I fill my dog's kong toy with peanut butter and only give it to him ONLY when he's in his crate. He nows RUNS and gets into his crate in the mornings when I leave for work. Also, make sure you don't use crate to punish her. It'll stop eventually! Still working on training my dog not to bark at night... he wants to come to bed with me! It's hard to ignore his cries and barks especially living in an apartment, but it's a must to train him!
