Undergraduate Publishing Options
What options do I have for publishing in an open way without expensive costs?


This is highly field-dependent, but there may possibly exist journals out there which will publish open-access for free. In my field it's common for papers to be embargoed for 6 months or a year, and then made open access, but again this varies from journal to journal and from field to field. 


  However, since ArXiv is not a journal, would it be considered incorrect or misleading to call my paper a publication if I were to post it there?


Yes. The correct term for a paper that has been posted on the arXiv is "pre-print". This is not the same thing as a publication. To call your paper a publication it needs to have been published in a (reputable) journal i.e. to have gone through the peer review process.


  Is it frowned upon or does it look bad if I use my personal Gmail account for contact information?


This would be pretty unusual, and as a reader I would think twice about the legitimacy of the work if a personal email address was attached-- in fact (I may be wrong on this) but I believe you need an academic email address e.g. name@place.edu or name@place.ac.uk to submit to arXiv in the first place.

My advice: talk to your line manager at the company and make a case for publishing the work. It seems strange to me that they have had you write this paper but won't support publishing it.

I think it's also a good idea to talk to a member of academic staff in your university department if you can-- all the better if their area of expertise is related to your paper. Ask their advice about publication in your field. It may even be worth asking if they have time to read over the manuscript draft and provide some feedback.