Is it possible to publish a research paper as an independent undergraduate author? I am interested in a new fast moving field in which none of the professors at my university have an interest. I have even started to work on some areas that show promise in the current scenario.

As I am working independently, and this will be my first paper, do I have a reasonable chance of getting it published (assuming it turns out well)?

What mistakes should I absolutely avoid while working on this paper? (to maximize chances of publishing later on)
Your question contains three questions. Is it possible? yes. Do you have a reasonable chance? Probably less than any other researcher because you lack the training but not zero. What mistakes to avoid? Well, that is what research education partly is about.

Writing a paper involves many aspects, providing the proper background, explaining the research, putting the research in perspective and reaching proper conclusions. There are many mistakes that can be made: you do not show you know the field, you do not describe the methods/theory/experiments well enough, your discussion does not hold and your conclusions are not well founded. All of this can come from poor understanding or from not writing well. So as long as you can tick the boxes from the subject specific to the methodological including writing skills then you would stand as reasonable a chance as any. In the end there is likely only one way to find out, try.

You state that you work independently and that is all fine. But, in science we all benefit from having others read and comment on our work to improve it so your chances of success can increase dramatically if your writing can be read and commented on by peers (with at least a PhD would be recommended) to weed out problems and any lack of clarity.