Department of Management Sciences, Pune University (PUMBA)

Yes, you are eligible for admission in PUMBA.

Admission is not based on candidate's family income, it is based on how many marks you get in CET.
Also there is no fees for NT category students.

As per last year, average package for operation is 5.5 lpa.

Last question first, PUMBA is a university department of Management Sciences which is autonomous. and NO we do not have foreign study tour. PUMBA has some excellent faculty for finance so its good for finance too.
Regarding percentile you have to check last year DTE's website, i think around 96-98 percentile will get you through!

Follow the procedure as directed by DTE. You will have to apply by both maharashtra seats and all india seats.

Placements in PUMBA are really good, come here and you will realize it!
The average package far all the students across all specialization is about 5.5 to 6lpa.

it depends upon how much experience you have

You can get into PUMBA by giving various MBA entrance exams such as CAT CMAT MH-CAT etc. and while filling option form choose PUMBA.Cutoffs are displayed on DTE's website http://www.dtemaharashtra.gov.in/MBA2015/StaticPages/HomePage.aspx

Separate applications need not be sent to PUMBA. All the students get admissions through DTE.
For out of Maharashtra students CAT, CMAT, MH-CET MAT are accepted. Cutoffs are generally high for OMS candidates and vary according to exam given

Your score is good in both MAT and CMAT. As last year's cutoff was 93%ile, score well in cet and you can get into PUMBA.