senses: this word refers to the 'five senses': sight, hearing, touch, taste and smell.
Sense (as in intelligence and good judgement). We don't really use 'sense' on its own. We talk of good sense, or 'common sense' (idiomatic). 'Out of sense' does not collocate well.
There are many other meaning of sense. Can you tell us which one you intend so that we can be more accurate in our responses?
Anyway, to look at your sentences one by one.
People should have normal human sense. This does not sound natural if you mean the good judgement meaning.. People should have good sense. ok. People should have common sense. ok. If you meant the five senses meaning then you need to say sences and not sence.
He has normal human sense and thinking. Would you say 'He has thinking'? This is incorrect. You need to use something like 'intelligence' instead. Again, the normal human sense is incorrect, you need normal good sense, or the five senses.
That is beyond man's mind and sense. The mind part is fine but sense does not work here.
How could he work with an immature human nature or with a deficient sense? immature human nature doesn't work as human nature is just what everyone has, it can't be mature or immature. We normally talk of personalities in that way. Again, 'a deficient sense' doesn't work on its own. A deficient sense of smell, yes. A deficient sense of justice, yes. Just a deficient sense, no.