お休みのところありがとうございます。って英語でなんて言うの？

The format: "Thanks for + VERB ing ..." is useful when you wish to thank someone - or say something sarcastic:
"Thanks for ruining my day!"

To be grateful for something or someone means that you are happy or thankful. It's just like saying thank you, but a little bit more formal. For example: I'm grateful for you taking the time to teach me on your day off. You can also use the word appreciate in a similar way. I appreciate that you have decided to teach me on your day off.

For this situation, you can show your gratitude by using words like "thank you" and "appreciate". The word "appreciate" shows that you understand they made a sacrifice to teach you, and you really thank them for it.

"free time" is another way of saying their "day off" or "non-working time". It is time they would have to freely do what they want outside of work.

Both of these phrases have a similar meaning. If we have to work on our day off, we usually say that we are giving up our day off. Meaning, we will not longer have our day off due to work. If someone gives up their day off for you, it is usually quite a big gesture so it is polite to thank them.

If the person was not supposed to work that day, it can be called a rest day. Since they are teaching you on this day, they are working and therefore gave up their rest day for you. They are also helping you, so you can also thank them for that and call it a day off. Lastly, you can express your appreciation for their sacrifice of their time off for your sake.

The sentences I have provided above all express how happy someone is with their teacher for meeting with them on their day off.