I don’t have a residency and don’t live in Portugal but I am invested in a fund.
Does it mean that I need to file any declaration in Portugal or maybe I can simply pay all my taxes where I live.
I assume QEF and M2M tax treatments are for the residents but I am not sure.
Those designations are for US based taxpayers. You don’t need to do anything in Portugal.
If you are on the ARI or golden visa you are not taxable in Portugal and you do not need to do anything related to Portuguese tax law. If you are a US Citizen, please speak with your tax advisor (assuming your fund is giving you positive returns).
Gotta love your confidence 
This has nothing to do with my confidence. I have this information in writing from my lawyers as well as the bank and the fund managers. Do you feel it is inaccurate or misleading?
Yes, it’s inaccurate.
The ARI program does not provide tax advantages - if you aren’t taxable in PT, it’s because you don’t pass the “is a tax resident” test (generally, > 183 days in PT a year, and not your primary residence)
Yes, as @garrett already responded, your statement was inaccurate.
Holding ARI in no way exonerates you from paying taxes in PT, these are different matters of residence permit vs. tax residency etc. albeit interconnected. It is even more complex that >183 days as PT tax residence can be held with 0 days presence in-country technically.
Your lawyer may have been correct regarding your individual situation, but it is certainly not applicable to any and all cases of ARI holders.