IGNOU - Indira Gandhi National Open University

IGNOU is a international reputation board. You can do anything as you want in it's degree.

You can take direct admission in IGNOU.

SOL doesn't have specialised course in B.Com for ICAI students whereas IGNOU has. It would be better to opt for IGNOU course specifically designed for ICAI students.

Yes, IGNOU has international reputation. It course material is of international standards. You can go for it. However, to enroll for MA one should have completed graduation.

You are eligible to seek admission in BEd at IGNOU if you meet following eligibility criteria:
(a) at least fifty percent marks either in the Bachelors Degree and/or in the Masters Degree in Sciences/Social Sciences/Commerce/Humanity. Bachelors in Engineering or Technology with specialization in Science and Mathematics with 55% marks or any other qualification equivalent thereto, and
(b) (i) Trained in-service teachers in elementary education. or(ii) Candidates who have completed a NCTE recognized teacher education programme through face-to-face mode.

All degrees, Diplomas, and certificates issued by IGNOU are recognised by governing authorities. Here is a link for you to go through:-
http://www.ignou.ac.in/ignou/aboutignou/division/srd/new
So don't hesitate and join IGNOU.
All the best.