1. luchar, lidiar, pelear, combatir;
These are all quite equivalent. I suppose the biggest difference is that they take different prepositions: luchar contra algo, lidiar con algún problema, pelear(se) con alguien, combatir alguna enfermedad.
2. tauromaqui, toreo;
TauromaquiA (you missed an A) is the name of the "art" (more of a bloody craft), and toreo is the actual activity. A bit like música vs. canción.
3. malo, malvado, maligno, maléfico.
These are all similar. Malo is just "bad", objective and without any judgement. Malvado is more than malo, it has bad intentions (applicable only to living beings, since objects can´t have intentions). Maligno is not only malo, but it also spreading or irradiating its "badness", like a tumour, or the devil ("el Maligno"). Maléfico is a more literary and dramatic version of malo, the type of adjective used with wicked witches.