M.Com

Yes, you can pursue CA programme, but according to me that will not a wise decision in term of total duration of programme is 3-4 years and you have to give full attention and time too for study to crack the exam.
In other case you can plan for MBA-finance that will be complete in next 2 years from good b-school and you can see your career with good growth and salary too.
Rest you can decide according to your career aim or interest.

No, you will only need to appear for only the subjects that you have failed in the reappear exam.

Preeti, you can not pursue two degrees from distance mode together. Yes, you can purse PGDBM from LPU, check the link below
http://www.lpude.in/programmes/frmMoreDetails.aspx?programname=Post Graduate Diploma in Business Management [PGBDM]&programcode=36

You are eligible to seek admission in MBA based on your educational qualifications subject to meeting other criteria. It is recommended that you may opt for MBA Finance based on your Accounting and Fiance background. Finance is the best MBA specialization after Marketing and it will open door of opportunities for you in Corporate world.

You cannot do two degrees simultaneously from same or different universities as per current UGC guidelines.

Please refer to the link: https://goo.gl/FVQoZb

You only have to reappear in a single paper. All the exams do not need to be re-given.