Applying for Applied Math PhD as a non-math major (Letters of Recommendation, etc.)
Having some research experience is better than no experience.  I don't see an issue with having a history professor write a letter for you, especially since you got research experience under their guidance.  Same goes for the economics professor, since Applied Mathematics and Economics are two very connected fields (and also since you wrote a research paper with them).  I think you should be good on letters of recommendation, especially since you mentioned that two of your potential writers are from past research experiences, which is what PhD programs want since it's focused on research after all.  As far as the professors you choose, it's most important to choose the ones who think most highly of you in a research setting, as opposed to &quot;got an A in my class,&quot; since PhD programs are about research output and less about A's earned in coursework.
The finance major shouldn't be too much of an issue.  Applied mathematics, as far as I'm aware, overlaps with many disciplines, ranging from quantitative finance to computational science to biostatistics.  Many of the professors in my department come from a wide variety of backgrounds, such as chemistry, physics, and pure mathematics.  So long as you have the mathematical basics to succeed you should have no issue here.
Finally, as far as other issues go, generally this is either for your SOP (Statement of Purpose, for talking about your research fit/interests) or something you should contact your programs of interest with regards to (including for the issue with the Math GRE given the circumstances we are in).  If you want to keep doing research, I know some professors (at least at my institution), have shifted to virtual format for the time being, you could try and see if there are profs doing virtual research in your school.
Hope my answer helped, especially for the LOR's part since that was your main point in the question, and best of luck with applications.