Hell
In the interests of strengthening your argument, I offer these criticisms.
I think you make a mistake right out of the gate with 1., which I take to be the premiss of your argument. Surely you would concede that there are things which exist but are not in the bible? Like black holes and many varieties of living creatures, hell could exist as well. This seems to dispell your premiss entirely.
I think 2 would be stronger if you made a distinction between differing states of existing, rather than restricting existence to exclude purely mental phenomenon. It is clear that things that exist conceptually still exist, so 2. will serve objections to your arguments if you structure it the way you have.
3. Is a pretty safe claim as far as I can see. There may be some wriggle room for interpreting the bible as alluding to a hell, but you seem to have largely countered this with some of your preamble before you stated your argument itself. (By defining hell specifically). You might want to include that as part of your argument structure somewhere.
Your conclusion in 4. doesnt follow from 1. In my opinion. I think what your argument accomplishes is concluding something like:
4. Therefore, concluding that hell exists based on a purely biblical account is not a reasonable conclusion.
I think you would still have some work to do if you want to make an overall religious argument against the existence of hell, there are biblical basis for accepting claims of hell existing from the clergy or in non-biblical religious texts and you would have to address those as far as I can tell.