Can I opt directly for second year B.A. in Mumbai after completing Diploma in Teachers Education? If yes, then from which institute?

Most colleges do provide lateral entry to Diploma students. Almost all colleges in my area have this system. If you are looking for colleges in your area, then I suggest approaching the colleges personally.

After completing Diploma first see whether you are eligible for any teacher exam? If you are then you go for that bcoz no age limit for doing B. A.