Can I publish a paper with a group that is different than the one I start with? I am an undergraduate who did research at my university a little while back. It was funded by a non-profit research organization, and I was paid with this money, through the university. I worked alone, but received some advice from people I worked with along the way. At the end of my time with the group, I had a poster with my findings on it, and I was preparing to begin writing a paper on the material. Unfortunately, the head of the group was let go from the university for some some immoral behavior (I'm aware that this is vague, and it intentionally so), and the group was disbanded. The university said that they would try to help me find someone else that I could publish with, but that never happened. 

So here I am, sitting on some work that I'm very proud of. I don't want for it to go to waste, but I don't know if publishing my findings with a different group, outside of my university, will be considered plagiarizing. Any advice? 

Edit: removed a separate question, asking how to bring the research up in applications
There would be no reason why it would be considered plagiarism—you've done nothing wrong. Getting another group somewhere else to help you get this work published would also not be considered unethical, so long as they actually make meaningful contributions to the paper.

However, if you've done the work all by yourself, why not consider publishing the paper by yourself? Many disciplines have undergraduate journals that would allow you to publish papers without being "sponsored" by a research group.