NIOS 12th

A learner of NIOS of 12th has the option to change in one or more subjects, provided the total number of subjects does not exceeds seven. However, such a change is permissible within four years of registration, so that learner can appear in Public exam within the validity period of admission. No change/ addition is allowed in the first examination. Subjects already passed cannot be changed. So if you are appearing in you first examination than you cannot change. However, after the first exam you can change your subjects. Please read NIOS FAQ for more clarity.
https://d39vpsp5tn2021.cloudfront.net/static/dist/images/pdf/NIOS_Faqs.pdf

Yes you can appear in NIOS for 12th Math subject. You need to apply ON DEMAND EXAMINATION if only 1 or few subjects you want to apply for. The basic concept of On Demand Examination is that NIOS Student can walk into the examination center as and when he/she feel ready for the examination. There will be no On-Demand Examination during the month of April, May, October and November. For more details please visit https://www.nios.ac.in/on-demand-examination.aspx.

Yes, you can. The NIOS board is recognised by MHRD government. of India. Hence, its all courses have the full validity as other educational boards. Therefore, you will get admission here in asked course if meeting the other eligibility criteria.

The NIOS fee for 5 subjects for Sr. Secondary course (12th) is about Rs 2000/ for general Male category, While Rs 1300 for SC/ST/PWD/Ex Service men. For each additional subject you have to further pay Rs 720.

The education eligibility criteria for army in NDA is Passed class 12 or equivalent examination from a recognised board and same for airforce and navy is Passed Class 12 or equivalent examination with Physics and Mathematics
and if your age is in between 16.5 and 19.5 then you are eligible for applying in NDA.