Are pianos played in the orchestra?

Yes, Pianos can be part of orchestras, they are in the percussion section, however the majority of orchestras do not include piano in them.

Yes, it would certainly be safe to say most orchestras have a piano; in fact, some classical pieces feature the music of the piano: these performances are called "piano concertos." There are some small orchestras that may focus on strings and woodwinds (like flutes or clarinets), but nearly every concert hall does have a piano.