What's the difference between 모르다 and 몰라하다? Some adjectives can form verbs by adding -어/여/아 하다, but in this case, 모르다 is verb.
For 모르다, you can refer to a dictionary.
몰라 하다 is almost always used in the phrases 어쩔 줄 몰라 하다 and 어찌할 바를 몰라 하다. These phrases can be used to talk about others who are at a loss to know what to do (You feel that they are at a loss because of their actions or facial expressions). Normally, you should use 어쩔 줄 모르다 to talk about yourself because you know yourself.
- You can also use 어쩔 줄 모르다 to talk about others when you use this technique.
- You use 어쩔 줄 몰라 하다 to talk about yourself when you regard yourself as others.
- You use 어쩔 줄 몰라 하다 to emphasize your actions and expressions rather than the fact that you are at a loss to know what to do.
You may have thought that -어하다 should be used with an adjective to indicate that the subject has a feeling toward the object (reference 1). The reality is that some verbs have qualities of adjectives and people attach -어하다 to a few (I mean, psychological ones) of such verbs. For example, 당황하다 is a psychological verb; you may have seen 당황해하다 as well (reference 2). 모르다 alone is not psychological, but the phrases I mentioned above is psychological. The standard dictionary does not deal with this case; the reason seems to be that they have not determined the spacing rule (reference 3).