UNIPUNE - Savitribai Phule Pune University (SPPU)

Yes, sure if you want to do graduation in that and want a degree in it. But if you are less interested, don't do it but don't even leave your music as it should be continued.

No, you do not need to appear for the UGC NET exam after completing MBA in technology management. UGC NET is conducted twice a year in order to select candidates for only Assistant Professor or both Junior Research Fellowship (JRF) and Assistant Professor in Indian universities and colleges. Unless you are planning to join the teaching line, you do not need to appear for the UGC NET.
Regards.

Yes, why not. Although just few seats are there for non Maharashtra students, provided to those who have good scorers. Roughly they accept around 97% from general category students. 65% intake is on the basis of MHCET and 35% on the basis of CMAT/CAT. Rest, for fair cutoff, check on official website.