You can buy a property here just as you would in the US...paperwork and terminology of the real estate transaction might be slightly different to a US citizen...but is essentially the same process.

As far as owning a business in Jamaica...the company will need to be registered and for a bed and breakfast they will need to be licensed by the JTB. They will also be required to get a work permit if they plan on actively running the business while in Jamaica or plan to spend longer than approx. 6 months in a calendar year.
If your friends plan to be here less than 6 months in a calendar year and have hired employees to run the property/business for them, your friends will not be required to get work permits...but they will also not be allowed to actively work on that property while they are in Jamaica.