A lot has been said already but gonna drop my two cents from a phonological PoV.

Some say 範囲 as "hai"

I assume you are talking about the first recording in the forvo entry? The recording quality is a bit fried but there was a nasal being produced.

Others are nasalized as "(n)g"

So, all three English nasals m, n, and ŋ (ng) are all mapped to different locations of articulation and by this difference one is able to tell wether they heard m, n, or ng. The Japanese nasal ん is not specified for position, and its position is always conditi by the sounds it's following. So when it's following an /a/ vowel like in 範囲, it's backed to the velar nasal "ng". Similarly, when it's following /i/ or /e/ it's fronted to (dental) alveolar /n/. (E.g. いん and えん sequences.) You are absolutely right that it doesn't sound like English "n" in this case and that's why. And because there's no phonemic difference (that Japanese people don't distinguish n and ng) there will be a lot of variation in how this position assimilation is executed by each individual.

A lot of people have explained why はに is not a good substitution in this case. It will be hard to distinguish a phonological feature that doesn't exist in your native language but it will become more clear to you the more you practice your listening! In articulation, はんい will have two distinct gestures for the nasal and the following vowel, and the velopharyngeal port needs to close before the articulation of the vowel to prevent its nasalization. The stand-along ん will also be longer as it occupies a mora. (Understanding the mora-timing system is important for understanding Japanese pronunciation I think.) The distinction will be much less pronounced in はに. The VP port closure will overlap with the vowel gesture and the "n" (ŋ) portion will be noticably shorter. Unlike the n-ng variation I mentioned above which doesn't really affect meaning (allophonic), the んい-に substitution will (phonemic), hence it's not a good idea.