usage

Thank you very much for your inputs

<<"I have done MBA" is grammatically incorrect. >>

I wouldn't say it's "grammatically" incorrect. But usagewise it is incorrect.

You could say (and I believe you may actually mean): "I have done [work on/toward my] MBA", which is fine.

'I have done an MBA' is correct.

I disagree. I'm only comfortable with "I got an MBA" or "I graduated with an MBA."

So do you also disagree with "I'm doing a BA right now, next year I plan on doing an masters program"?

Yes. I disagree with that usage. "I'm working on a BA right now, next year I plan on starting my master's."

I got my BA last year and next May I'll get my Master's.

I can't think of a situation in which using "to do" would work better. I don't think it works in this context.

If I heard someone say, 'I have done an MBA' I would immediately notice that the person is a non-native English speaker. I also would think that someone who says, "I did a BA in English" is a foreigner who learned English as a second language. I would certainly respect that they were able to obtain the degree in what is for them a foreign language, but the awkwardness of the useage would give them away as a non-native speaker of English.

Тhat's strange! "I did a BA in English" sounds absolutely 100% natural to me and I've heard people say things like this countless times (I work at a university in New Zealand).

"I did a BA in English" sounds odd to me... I'd favor "I got a BA in English."