Go out of one's way to do sth

Hi~teachers.

I've come across this expression in the dictionary.

I was looking for the expression but I am not sure if it is quite common.

Q1. I am wondering if it's ok to use this or there are more common expressions.

Let's say there is sb who always tries to go strait home while other friends want to hang out.

So I'd like to tell tham sth about it. (We ask if they have honey at home in Korean in a funny way)

Q2. Is there any slang or idioms for this situation?

I have a friend who always eats Korean food

but when she meets others she is willing to give up what she likes and tries to look on the bright side saying like

"I always eat the same type of food so it's ok (refreshing) to try new one sometimes because it's not sth that happens all the time."

Q3. Is there any slang or idioms instead of what she said?

One of my students asked me a question about "back-working work."

Her native English-speaking teacher wrote this and I don't know what it means.

My student were talking about her back injury from doing housework.

Q4. Would you let me know what it means or if it is just a misspelled expression?

Sorry for the many questions.