Can I publish in a field completely unrelated to my present field? If yes, what about affiliations?
Should you ever include people as author for liking your manuscript? No!

Can you try to get in contact with an academic of your favourite field, discuss your ideas with him/her and ask if they'd like to write a publication with you? Sure thing.

Will publications in a foreign field hinder your main Phd? Depends. 

Will you find the time to do both in parallel properly? If not, which has preference? If you do it before you start your main PhD or you are happy to develop that other paper slowly as a hobby, it may not affect your main work. 

Will it affect your reputation in your main field? For most people it should not have any impact at all. A few may value your additional interests others may see this is a diversion or as a potential risk for you to jump ship and switch your research areas. But overall, I'd think those are few and they'd even themselves out. 
With respect to industry, many recruiters even claim they look for candidates that do something unconventional as a hobby/side interest. So in industry you may even win some minor bonus points.