1) What is the tone poem and who invented it?
Difficult to define, but you could trace tone/symphonic poems and other romantic programmatic music all the way back to the Baroque (cf Vivaldi’s Four Seasons) and even earlier.
But the tone poem as we know it started somewhere in the mid 19th century with Franz Liszt.
2) What key is rondo always heard in?
The rondo (‘round’, in the form of ABACA…ABA) often is the last movement of concerti and sonatas. In these cases then it will usually be written in the same key as the first movement.
There is no specific key, though.
3) What is the fixed idea (indee fixe)?
As far as I know the idee fixe started with Hector Berlioz’s Symphonie Fantastique, where a melody (and its variations) appears throughout the entire piece as a symbol for the girl that the hero in the symphony is infatuated with. (The work is a piece of programmatic music)
4) What is verismo?
"A style of operatic composition, prevalent in Italy in the 1890s, with repercussions extending to other European countries and later decades. Verismo in Italy originated in Milan in the 1870s, when the Sicilian critic and writer Luigi Capuana published the novel Giacinta, generally regarded as the “manifesto” of Italian verismo. The most important and influential exponent of the verismo school was Giovanni Verga, whose novel and plays show analogies with the naturalism of the French authors Emil Zola whose novel Germinal portrayed a coal-mining community living in terrible housing, working under shocking conditions, and a major pit accident and rescue, and Guy de Maupassant.
… The term verismo is used more loosely to describe opera that portrays “everyday” characters. …"
5) What generes and forms did Mendelson compose in?
Felix Mendelssohn: symphonies, concerti, songs, sacred music, incidental music…a very prolific and talented composer. The only major genre that he did not compose in, IIRC is opera.