The ideal is to back-test using the broker server data.

The  data that is downloaded  automatically form MT4 comes from Meta-trader's server NOT the dealer server.
SO this files are converted automatically and internally in MT4 under c:\\ ***\tester\history , and the form of the file is ".FXT".

My question then is..Any backt-esting  done in MT4 will not replicate the dealers data but only the Meta-trader data. So the Back-testing is lacking reality in this case. Correct?

In FSB we can update the Data with the real data form the broker and run back-test, the back test using FSB will be accurate in real life and the back test in MT4 will only somehow replicate the result with multiples errors, that is my understanding.

I need to re-confirm these analysis to avoid future mistakes and be cautious about the back-testing in MT4

Please advise.