Sometimes in songs I see sentences in present progressive without verb to be, like - she getting down. Is it right?
Asking whether this is "right" is a tricky question in linguistics. There are two ends of the spectrum for viewing language, one being prescriptivism and the other descriptivism. The former has connotations of a 19th century grammar school teacher that will rap your knuckles for misspelling a word, while the latter can be thought of as a brilliant alien who comes to earth to observe and record the language it encounters in ALL settings (registers) to present the data to its own people back on its home planet.
From a descriptivist standpoint, the phenomenon you're observing here is called Zero Copula and is in this instance likely a feature of the African American Vernacular English dialect (AAVE; sometimes referred to as Ebonics). It is a recognized, spoken dialect that has observable patterns and rules—so much so that the Holy Bible has been translated into this dialect.
A genre of music (that includes spoken word) will often adopt a characteristic dialect based on the genre's origins, so that you even see artists whose native dialects are not the same as that of the genre's, writing lyrics that fit that of the genre (e.g., Vanilla Ice).
Your question as to whether this grammatical construction is "right" might be rephrased to, "is this Standard American English?" The prescriptivist answer to that would be: No.