None of Beethoven's symphonies has a piano part. He wrote five
concertos for piano accompanied by orchestra, and a Fantasy for
piano, chorus and orchestra.
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It's the violin, piano is rarely used in orchestra pieces.
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No, a piano is an instrument. An orchestra is an ensemble of
different kind of instruments. The piano does not have a place in
the average orchestra. It may however play with an orchestra in a
concerto. Pianists can also play arrangements of orchestral
pieces.
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In a typical orchestra, there is usually one pianist who plays the piano. The piano is considered a solo instrument, and the pianist performs independently of the rest of the orchestra.