Insight checks are non-magical.
The description only states that you're immune to magic that does those things. However, an insight check is not magical (PHB 178):
Your Wisdom (Insight) check decides whether you can determine the true intentions of a creature ... Doing so involves gleaning clues from body language, speech habits, and changes in mannerisms.
Thus, the ring does not protect you from ordinary, non-magical insight checks.
As for DCs, there aren't any specific rules as to what the DC should be. Given that the interaction is wholly nonmagical, I usually use a contested deception vs. insight check when a scenario like this arises.