No you are eligible only for the Delhi counselling since you have completed 11th and 12th from Delhi and your father being in the army you will get reservation under CW quota in Indraprastha University counseling for MBBS.

You will get only one domicile otherwise.

Yes, you can apply for Delhi state counseling as you completed Class 11th & 12th from Delhi.

For Rajasthan, you may be eligible since your mother has a Rajasthan domicile, but it depends on state rules.

Most states allow only one domicile for NEET counseling, so check Rajasthan’s latest criteria before applying for both.