フリーカンバセーションでお願いしますって英語でなんて言うの？

If you want to use 'do,' this refers to the content of the lesson, so you need to name the element that you wish to pursue. For example, algebra, trigonometry, exam questions, pronunciation, reading or ............... free conversation. 'Free chat' seems like an Eastern term which is never heard in the UK. 'Chat' means, 'talking freely,' so the word 'free' is unnecessary. It's like saying, "I'm going to have a wet bath." All baths are wet, so there is no need to say it.

Can we just have a casual conversation today? No serious learning please! How about us talking freely today! I'd prefer that to a lesson!

Normally, the beginning of your lesson will be a quick catch up, "did you have a good day?" "What did you do over the weekend?", etc. So then if the teacher asks you what you would like to do in the lesson, because you are already having conversation, you can say "I'd like to continue with free conversation".

If you are talking about having a lesson then you can say 'Can we have' or 'can we do' Also you can call it 'free conversation' or 'free talk or talking;' these all mean the same thing and your tutor would know what you mean and want to do. By adding please you are asking politely/nicely

Native speakers will say like this: “Can we have a free conversation for this class”. There are lots of other ways to say it, but this one is the most accurate and most commonly used. Here is an example on how to use this in a conversation: A: Teacher, can we have a free conversation for this class? B: Of course! Do you have any topics in mind?

You can use "would like to."(Your preference) When you say "could we?" (You are asking the teacher if it is okay) Example : A : What would you like to do in today's lesson? B : I would like to have a free conversation. OR C : What would you like to do in today's lesson? D : Could we do free talking please?