What are your plans for after you earn degrees (particularly undergraduate - BA or BM) in music? I heard that only less than 25-30% of undergrads will be able to get into the master programs because of extremely high competition...if that's the case, how will the career for the remainder be like (i.e., type of jobs)? Is it recommended to finish up to the graduate programs in order to pursue music to make money?
This is because, since I will turn mid-30s at the time of completing my bachelor's program, I think I will need to seriously think about searching for jobs right after then...and if it is still possible to get any jobs with reasonable earnings then it's even better to start working without continuing studies for the graduate degrees...
Are there any jobs or positions also open to undergraduate students? Any help or comments will be appreciated 
Where do you find this figure of 25%-30%? The acceptance rate heavily depends on the caliber of the graduate program. For example, many students who are not accepted to the DMA at IU end up pursuing the doctorate at another conservatory such as Eastman or Oberlin (the IU doctorate entails eight recitals, four seminars, and several other requirements and takes four to six years to complete; SUNY Stonybrook, on the other hand, generally requires no more than three years to complete). I think also that this percentage is a result of students' desire to continue their education, and not only their ability.
This having been said, there is quite a bit open to those who have not pursued advanced degrees. In truth, it is really only for teaching jobs that graduate degrees are required (though this is not always the case). Some of the many possibilities for those with a B.M. alone are pre-college teaching, freelance accompanying, concertizing (usually expedited by competition laurels or emergency substitution), recording engineer work (with additional knowledge), piano tuning (again, with additional knowledge), arts administration, music journalism, and other miscellaneous jobs such as engraving, transposition, arranging, and keyboard programming for musical theatre.
While it is beneficial to continue education, a good pianist is a perpetual student, with or without a master teacher and under or free of the auspices of a formal degree program. It is always possible to advance one's knowledge via critical thinking, constant reading, attendance at master classes and festivals, collaborative work, listening to recordings, and of course, good-old-fashioned practice.
I myself will begin an M.M. in the fall, but really only for the knowledge and for the possibility of pursuing doctoral studies if I should want to in the future. Regardless of degrees, my career plans remain the same - to be a good piano teacher and active collaborative pianist.
Hope this helps!