Rushing for more than twenty yearsFor over twenty years, he traveled back and forth between Europe and the US and giv, performing abroutnd 60 concerts a year, he would become a renowned virtuoso pianist, each time gathering a full house at his performancesnnually. His performances consistently attracted full houses, establishing him as a renowned virtuoso pianist.

Although he would not abandon composition for good, during his last 25 years, he would write only 6 out of his total 45 opuses in total.

As the composerRachmaninoff confessed, that he could not combine composing withdo both: compose music and givinge concerts. He said that he could not combine the two.

Rushing between Europe and the US for more than twenty years between Europe and the US and givand performing about 60 concerts a year, he would become a renowned virtuoso pianist, each time gatheramassing a full house at his performances.

'gather' works great, but 'amass' is slightly more elevated.

Although he would not abandon compositiong for good, during his last 25 years he would write only 6 out of his total 45 opusesera.

I admit that I don't come from a musical background, but I think of 'composing' as the general artform, and 'composition' as the individual musical piece.

The plural of 'opus' is 'opera' -- often words that are directly borrowed from Latin also inflect plural verbs differently.

He would only write music only during his summer vacations at his Villa Senar in Switzerland.

The previous position is correct, but 'only' in this position sounds better to my native ear.

In 1934, it would be a 'Rhapsody on a Theme of Paganini'.

Individual artworks are always in single quotations.

The last of Rachmaninoff's concertante and piano works is an acmethe height of his mastery of the piano.

'acme' isn't very idiomatic in this context.

After the loss of thehis motherland, a main source of inspiration for Rachmaninoff, he could no longer celebrate the simplicity and sincerity of Russia and its people in his music.

In 1934, it would be a he wrote "Rhapsody on a Theme of Paganini".

Rushing for more than twenty years between Europe and the US and givbetween Europe and the US for more than twenty years and performing about 60 concerts a year, he would become a renowned virtuoso pianist, each time gathering a full house at his performances every time.

Although he would not abandon composition for good, during his last 25 years he would write only 6 out of his 45 total 45 opuses.

As tThe composer confessed, that he could not combine composing with givperforming concerts.

Not grammatically incorect, but "As the composer confessed" seems strange because we conflate "confessing" with admitting a crime or telling someone you love them, but it could be some kind of admission that is rather negative. It might be best to add context as to whom he made the confession toward. It could also be better to simply write the sentence in a matter of fact manner: "The composer could no longer combine composing and performing concerts."

In 1934, it would be a Rhapsody on a Theme of Paganini.

Not gramatically incorrect, but a bit more context is needed to connect this sentence with the previous one. Something along the lines of "There in 1934, he would write [his magnum opus], Rhapsody on a Theme of Paganini."

After the loss of the motherland, a main source of inspiration for Rachmaninoff, he could no longer celebrate the simplicity and sincerity of Russia and its people in his music.

Alternately: "After the loss of his motherland. . ." can also be used if you want to present a more personal attachment in the writing.

He had no choice but to concentrate on the memories of the past and observations of the new post-war world: decadent modernism, inevitable technological progress, and the ubiquitous worship of Mammon.