And while Normal is weak to Fighting, there are both strong Normal attacks with high accuracy and many good Normal Pokemon, defensively. It has an immunity, which is always nice, and only two types resist Normal damage. Making it a very good offensive type to use.
Using your logic, it shouldn't make sense that normal is NVE against Steel and Rock since it is "typeless"
Then Rock and Steel shouldn't resist it either.
Ah, good catches. Let me rephrase that, then- Normal is more or less the "regular" type. Regular attacks are less effective on the hard-bodied Rock- and Steel-type Pokemon and they have no effect on Ghost-type Pokemon. It also makes sense for regular attacks to not have any sort of advantage on anything.
only two types resist Normal damage. Making it a very good offensive type to use.
Nope. Normal's offensive coverage can be generously described as "meh". Two types resist it and another is immune. Know what types have it better than that? Only about 8 of the remaining 16 types: Dark, Dragon, Flying, Ghost, Ground, Psychic, Rock, and Water. And Normal's even worse when you actually look at how viable different types are at affecting actual Pokemon that are powerful and widely-used; the popularity of Steel types is more than enough to attest to that.
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So do Fighting types, Ground types, Grass types, Ice types...
I suppose so... Ah well. I'll be pretty surprised in Normal ends up being SE on Fairy, but I suppose the logic would be something similar to one that explains the mutual immunity between Normal and Ghost...
I'm somewhat torn on it. On the one hand I'm all for Normal getting a slightly more balanced approach. As it is now it feels a smidge... bad in some ways. Not bad bad, just not as balanced as it could be. Having a super effective to balance that out, and other such things would help. However, I'm against it being Fairy myself, but that's as much because I'm worried about other hypothetical weakness it may have. Depending on the overall way it works out it'll be fine.
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Bad Idea. Anything that would usually be threatened by a Fairy type can just run Return for super effective damage - and everything that can use TMs can learn Return.
Fairy would become a rather poor type because of it - bordering on unusable in terms of casual play where everyone probably has some random normal attack on a bunch of their mons, and in competitive Fairy users would have to fear surprise Normal attacks from EVERYTHING.