Why is Bhairav / MayamaLavagauLa the first raaga to be taught?
Sri Purandara Das decided that "Malava gowla" of the South was most suited for beginners. The corresponding Raag in the North is called "Bhairav".
In "Malavagowla" subsequently named as "Maya Malavagowla", the difference of pitch between 'Re' and 'ga', and 'dha' and 'ni' are the same and the notes sa-re-ga-ma and pa-dha-ni-sa are perfect concordant notes. That is why Purandara Das found Maya Malavagowla the best Raag to begin lessons in classical music.
Why is Bhairavi / Sindhu Bhairavi usually the last last raaga during any performance? (Carnatic equivalent Madhyamavati is also used as the closing kriti).
Perhaps Bhairavi’s HIGH EQ (Emotional Quotient) makes it suitable for the finale!! Also, to the best of my knowledge, it is one of the "time-free" raagas (like Pahadi, Dhani, etc.,) and hence can be performed at any time of the day.
"Madhyamavati" (MEGH in northern classical) is performed at the end of concert since it is believed to "cure" all mistakes committed by performer during earlier performances! Madhyamavati is called "Sarva-raga-dosha-pariharini". In any case, it sets a very peaceful mood and is very much suited at the end.