I know it's so frustrating to potty train new pups, but it really does take tons and tons of patience.
I got mine at nine months and she STILL wasn't potty trained. She went in the crate AND she never went outside. She just didn't seem to understand what outside was for. I'd stand out there for over 30 minutes with her and I'd get nothing (and what made it even worse was it was the middle of winter with freezing temperatures, since I lived in a different state than I do now). It was so incredibly frustrating; There had been points when I seriously considered giving her back.
Not only did I have to break her old habits, I had to retrain her.
Here's what finally worked for me: I would pick up her poop or pick up her pee-soaked paper towel after cleaning it up (by the way, you can only tell her "No" if you actually catch her going to the bathroom where you don't want her to. If you tell her even just minutes after the fact, she'll cower but won't know what she did wrong), pick her up, take her outside and drop the poop or pee paper towel on the ground. Let her sniff there and say "potty." It took several times before it worked, but it was like a miracle for me. Also, I would catch her hunched over about to poop and I would pick her up, run outside and she would actually finish pooping outside. I'm not sure how your pup works, but mine would continue peeing on the carpet even if I would pick her up. lol It was awful. I finally started putting an empty plastic cup next to me so I could catch the pee in the cup and then take it outside with her, empty it on the grass and have her sniff.
Don't forget when she does go to the bathroom outside to have a key word or sound for her during the act. The hope is to eventually be able to make that noise outside with her and she will immediately begin going to the bathroom. Mine is "shh." LOL
Also, every time right before you pick her up to take her outside, say a key word so she knows it's time to go to the bathroom. Mine is "potty outside."
As far as the crate, you have to make sure she has enough room to stand up, turn around and lay down comfortably. If it's too small, it will cause major problems, but if it's too big, she will just potty in one corner of the crate and hang out in the other. Pups don't like to roll around in their own mess. Mine did the first few times, but she eventually learned she didn't like stepping in it. Plus, she hated the bath afterwards.
BUT crating is best for older pups. Since you have a very very young dog, I wouldn't really recommend crating her. I would put her in a little pen area with a blanket, food, water and a pee pad. She is much much too young and young pups just can't hold it for very long. Plus, you don't want them to because it's super bad for them.
I hope this helps! She's really really young, so it's just going to take some time. Just be thankful that they learn to be potty trained faster than skin kids!