Always: Bb soprano clarinets and Bass clarinets, sometimes: Soprano A and Eb clarinets, very rarely: other varieties of clarinet (piccolo clarinet, basset horn, basset clarinet, contra alto/contrabass, alto clarinet, etc.)
Bb soprano clarinets (the common Clarinet) and bass clarinets are always used in orchestras and bands. Orchestra music (bands not as commonly, but still sometimes) frequently call for soprano A and soprano Eb clarinets, so usually Bb players learn an alternate clarinet and play it when they're not playing the normal Bb part. Other kinds of clarinets, such as basset clarinet, tenor clarinet, and basset horn, are rarely used (not never used, just not nearly as commonly.) Alto clarinets are used much more frequently in bands than in orchestras.
Generally, 2 or 3
Orchestra, background music, the such.
usually near the trumpets and alto saxaphones
Yes, why, yes, there is.
A normal full orchestra would have all instruments except for saxophone and bass clarinets.
The organization of an orchestra is hundreds of years old and fairly universal. Clarinets sit with similar instruments (like the oboe, bassoon and flute) in the center of the orchestra.
Either solo or any type of band or any type of orchestra
There are all sorts of instruments in an orchestra such as: Flutes/Piccolos Clarinets Tubas Violins Violas Harp Trumpets Trombones French Horns Timpani Bassoons Saxophones (Tenor or Soprano)
Some instruments that are used in a chamber orchestra are bassoons, oboes, clarinets, flutes, and piccolos. Trumpets, trombones, French horns, drums, violins, and cellos are also used. A chamber orchestra will have between 50 or 60 instruments.
F. A. Hoffmeister has written: 'Concerto in E flat for 2 clarinets and orchestra (piano reduction)'
saxsbut, clavichord, viola, violin, cello, clarinets, flute, bassoon... any combination in trio works well and all together in baroque orchestra.
Wind instruments other than brass instruments forming a section of an orchestra, including flutes, oboes, clarinets, and bassoons.