Mrs. W, look up www.efax.com
they're the major player in that business.
You will come down to using a service, which you will pay for, that gives you a virtual fax phone number. People send faxes to that number, the service converts it to a JPEG or TIFF image and sends it to your email account. Or you can access it through the web, but with an email account it can push right out to your computer, and if your computer uses an email client like Outlook, it can be printed on the spot as well. Unattended.
There are other services, efax aka jfax is simply one of the oldest and possibly most reliable. Plenty of competition these days.
You send faxes back down the same pipeline, either create a document on your computer and post it to the service (by email usually) and they push it to a real fax machine.
As to using mifi or other cellular systems offshore? No, when you're offshore you will need satellite
internet and you'd better open your wallet and take a look at those options. Satellite internet.
Because anything cellular has a 3-mile practical limit, if that far, and a 32-mile technical limit, if you can find a provider who allows for the maximums their hardware
can deal with. Three mile maximum practical limit, no matter what you use. WiFi? Even less, when and where you can poach it.
Business use? Efax and cellular and wifi, you'll need to be equipped with both if you want to take advantage of all the options. And if you need it in realtime, really offshore, you'll need to look at $atellite internet connection$. Which oddly enough, don't cost anything more than plain overseas telephone calls did in the 70's.