If it is private, use that to your advantage, have a general grammar point and vocab area you want to cover. Have a few introductory questions. Build vocab with them, and then just drill, be really nosy and ask them a 1000 questions, making them use the new words in their response. You can fill 90 minutes with this pretty easily. If it's the first time I would do this with a general topic such as vacation, so that the question asking can never get too personal.
My first German teacher was Croatian. I think that she did a pretty good job but who am I to judge?
however, i think it would be arrogant for someone to think that being a native speaker somehow automatically grants him/her god-given abilities or, worse, rights to teach or teach better than non-natives.
also, no one can claim that they know everything there is to know to do their jobs, and learning is a life long process. the OP is moving from the classroom to the private arena, which would be a new experience, and is trying to bounce some ideas of the forummers here. given the amount of international teaching experience in EF, i think it's a good idea.
i found the bard to be quite painful at times, definitely not for everyone. discussion about the works, and not the prose, has potential... but only the exciting ones like macbeth, hamlet.
My German teacher - a native German, re-taught me plenty about English grammar I had forgotten.
I have no problem with the OP teaching that's their business and have no problem with English being a second language(some Indian friends speak better English than many English). However, I am a trained professional Art, English Language and Literature teacher who has spent years in Uni and have been teaching for more years than I wish to remember. This is not a teaching forum and alarm bells rang when I read the OP asking for ideas from folks here.. if you have never taught a student on their own before then go to a teacher forum and get advice from a professional who can really help you. As for working in teaching agencies here, yeah I've done that and quit a couple of them. I found out that a few of teachers were straight out of Uni with a degree with no training to teach and were speed reading prior to the lessons to figure out how to do it and coming to me and the qualified staff when they wanted ideas or were having problems. They got paid the same as me too, what an insult.. and don't be surprised when you get narky comments as this country is full of unqualified teachers, I've met so many I've lost count. So, my point being go and learn from the Professionals you will learn more and as for setting up a teaching thread.. give me a break.