I am doing BA English through TNOU open university. Am I eligible to take law entrance test for regular LLB?

LLB Eligibility: Aspiring candidates should have scored a minimum pass percentage either at the 12th level or graduation level. The percentages are 45% marks for General category, 42% for OBC and 40% for SC/ST categories.

As per my knowledge and experience for regular LLB, there is no such rules and regulations for any criteria that you must have done your graduation from open or regular. So, you need not to worry about it. You can proceed.

Yes, once you're done with your graduation you're eligible for LLB programmes. You can appear for various law entrances.