1, I understand that the question could be interpreted in different ways but regardless of how he spent the night with the concubine he still spent the night with a concubine and lied about it. He probably didn't do anything serious like you said and thought it wasn't important to mention but he regardless still lied about it. He failed to see the anxiety Tei had about it
2, given what the concubine said and that he laughed (pfft) after declaring the "main wife" doesn't need to sleep with Sharaka I doubt he ships the relationship. I could be wrong but you don't yell out a blatant lie like that unless you've been put under some impression you won't get f*cked up, which encouraging the "main wife" through rage baiting doesn't seem like a good reason to avoid punishment

Main character never asked that , did u slept with your concubine??? The question he asked was did u spend time with your concubine.
Which ml could interpret in few different way.
Possibile
Spend time : as in work , or getting tutored , lectured in the way of sex.
Then yes that pink haired and him spend time together.
Btw that pink haired bitch looks smug rather than irritated when mc declares he would help ml tonight. Meaning he is actually shipping them or he could just be snake with different agenta
What i gather
In mc back home , ml was clearly inexperienced we can gather by through his action. He said mc is his only beloved , he told no to the idea of concubines.
If in just one night after getting mc back his home country , he had sex with pink haired one. It would be way too hyprocritical.. No just low but way too much. Your words and action would be completely different.