How could Chana have been nistira?
The gemara on 30b explains that Chana said to Hashem that if you don't give me a child then I'll go seclude myself with a man and drink mei sota. The Pnai Yehoshua asks how could Chana threaten such a thing? First of all, there is an issur of yichud and second of all she is causing the shem Hashem to be nimchak! He answers that Chana never intended to carry out this threat. She just meant that it's unfair for Hashem to not give her a child because otherwise she could do this trick.
The truth is that the first question isn't really a problem. The dinim of stira are different than the dinim of yichud. It's possible to be a sotah without being over the isure of yichud. The first two halachos of the Rambam in hilchos sotah give two examples. One is if she's nistater with her father or son. There is no yichud but if her husband was mikane her with them then she will be chayeves to drink if she is nistater with them. The second is that if the husband was mekane her not to be with two men. There is no isur of yichud with two men but if he was mekane her with both of them together then there is a din of mei sotah.
I'm not sure about how to answer the second question except that I don't think there is anything wrong with erasing the shem Hashem in the case of sota. The gemara does talk about it being a bad thing but that's only if the mei sota is used in a case where it won't work. For example, if the husband was mezane then the mei sotah won't work and he's doing a bad thing by forcing his wife to drink. However, the mei sota was designed to be used in any case where there is kinui and stira so provided that he wasn't boel someone he wasn't allowed to (or any of the other reasons it won't work) she's doing nothing wrong by causing the shem Hashem to be erased.