Your question shouldn't be whether or not the “whys” are normal but whether or not you want them in a relationship. You should move the spotlight from your partner and shine it on yourself. You read this article about narcissists for a reason, but the only one you can change is yourself.
When children ask a lot of “whys,” they're showing tremendous curiosity about the world. However, I suspect you're not asking about someone who's displaying a curious nature but someone who's acting in a way you find darker and more disturbing. I suspect you're asking about someone who, in a passive-aggressive way, is challenging the way you do things (Why do you cook spaghetti that way? Why do you take so long in the shower? Why does it take you so long to get ready?)
The partner who uses “whys” in this way is implying: The way you do things is wrong. You should do them like I do. My way is better, smarter, more efficient, etc. This individual is operating from ego. It's a way for him or her to feel superior. In the process, though, it can make the person on the receiving end feel criticized, controlled, less confident and “less than.”
The best thing to do is have an open and honest conversation. Tell your partner that the “whys” are making you feel weird and causing you to doubt yourself. Then listen very carefully to the response. See if your partner is being receptive to what you shared, is offering insight into the behavior, and is expressing a willingness to change.
You want to be in a healthy, happy relationship where you communicate honestly and openly, can be vulnerable, and are your authentic self. When a partner questions our every move (over things both little and small), we can start to feel shaky. Sometimes that's their intention and sometimes it's not. If this is happening to you, I'm glad you've recognized it and can make a conscious choice of what to do next. Take care!