I work part of the year or the entire calendar year for a Puertorican Tug and barge company onboard their tugboats not ashore , I don't have any address in Puerto Rico, I reside in the US and just fly over when I'm called for a voyage or a job, and when it is finished I return back to my residence in the US mainland, can I report those earnings as a Foreign Earned income.
No, this is not considered foreign earned income.
The IRS defines foreign earned income as income you receive for services you perform in a foreign country during a period your tax home is in a foreign country (See: Foreign Earned Income.)
Your tax home is in the United States since this is where you reside. Report this income as you would any other income earned while a resident of the United States.
Can I exclude the income since it was earned not living, just working onboard vessels that operate out of P.R, and the company that operates and owns them is located, registered, and owned in P.R, being P.R a U.S possession ?.
Under certain circumstances, you can exclude income earned in the following possessions of the United States:
Commonwealth of the Northern Mariana Islands
U.S. Virgin Islands
That depends on your residency. According to the IRS, your residency can be anywhere that you intend to call home (and where you are physically present for a significant portion of time).
If you're a bona fide resident of Puerto Rico during the entire tax year, you generally aren't required to file a U.S. federal income tax return if your only income is from sources within Puerto Rico. However, if you also have income from sources outside of Puerto Rico, including from U.S. sources, you're required to file a U.S. federal income tax return if such amount is above the U.S. filing threshold. Nevertheless, a bona fide resident of Puerto Rico with a U.S. filing obligation, generally won't report Puerto Rican source income on a U.S. income tax return.
U.S. citizens and resident aliens who aren't bona fide residents of Puerto Rico during the entire tax year are required to report all income from worldwide sources on their U.S. income tax return.