But what if he neglect the care of his soul?
Quid tamen accidit cum homo amimum curare neglegit?
That is grammatically correct.
However, I might suggest a rewording:
sed quid si animi curam negleget?
The addition of
homo is unnecessary unless you want to turn the passage into a more self-contained one (since I assume the "he" of the English refers to a man previously mentioned in the original work). In that case I guess you would also do away with the "but", though, which also refers to something that came before.
I answer: What if he neglect the care of his health or of his estate,
Quid accidit, inquam, cum neglegit curare vel sanitatem vel possesionem
That is grammatically correct too, but again could be rephrased a little more simply as
Quid, inquam, si sanitatis possessionumve* curam negleget?
*Better in the plural.
which things are nearlier related to the government of the magistrate than the other?
utrae res propinquiores et necessariores magistratus gubernationi sunt quam altera?
This doesn't work.
The "which" you need here is the relative
qui, quae, quod. You can say either
quae res or just
quae in the neuter plural.
Necessariores doesn't fit the meaning.
Propinquiores alone makes sense, though the more usual comparative form of
propinquus is
propior. Instead, you might also say
magis pertinent ad.
"The other" is the previously mentioned soul, I believe, so it should be masculine to agree with
animus. Perhaps also
ille would be better quam
alter.
Will the magistrate provide by an express law that such a one shall not become poor or sick?
Magistratusne expressa lege jubet ne hoc homo vel pauper vel aeger fiat?
I think it would be good to keep the future tense here (hence I also used the future tense in the
si clauses above).
Hoc (neuter) doesn't agree with
homo (masculine).
Laws provide, as much as is possible, that the goods and health of subjects be not injured by the fraud and violence of others
Jubetur legibus, ut maxime potest, nec sanitas nec bona civium noceatur aliorum ab fraude et vi.
A better verb to use here in the beginning would be
providetur or
cavetur.
I think I would put
legibus first in the sentence because it seems an appropriate emphasis.
A more idiomatic translation for "as much as possible" would be
quantum fieri potest.
Your double
nec doesn't really work because you need a
ne to introduce the indirect prohibition.
Ne... nec... wouldn't sound very good here, though, so I would choose
ne... -que.
Noceatur doesn't agree in number with its intended subject. However,
noceo is usually intransitive, taking the dative rather than a direct object, so the more correct construction here would actually be with
noceatur in the third person singular impersonal passive and
sanitas and
bona in the dative:
ne bonis sanitatique civium noceatur.
"By" translates to
ab only before an animate agent. Fraud and violence are not animate and are truly closer to instruments than to agents, so
ab should not be used here.
they do not guard them from the negligence or ill-husbandry of the possessors themselves.
Leges non custodiunt eos ab negligentia vel agricultura mala ipius possessoris.
The most serious problems here are 1) that
eos is in the wrong gender: "them" refers to
bona and
sanitas, which, being two names of things of different grammatical genders, will be jointly represented by neuter pronouns by default; 2) the "husbandry" mentioned here doesn't have to do with farming, but rather with estate management. I don't know any exact word for this in Latin, but you could say something like
mala rei familiaris cura.
Now, to come to more subtle matters of sentence structure, I think you do need something to connect this sentence to what precedes, for instance:
verum leges non custodiunt... or
nec tamen leges custodiunt...
Detail: you could keep the plural of "possessors".
No man can be forced to be rich or healthful whether he will or no.
Nemo vi fieri potest dives vel sanus, utrum vult an non.
The original isn't so much about specifically
becoming rich or healthful. It's about
being rich or healthful. Being can include remaining as well as becoming. So I would translate "to be" literally, to comprise the same range of possible meanings as the original.
A good translation for "be forced" is
cogi.
Utrum... an... is used in questions. It's a different kind of "whether... or..." that we've got here. Not a question. This sort of "whether... or..." usually translates as
sive... sive... or
seu... seu... However, in this particular case, there's a different idiomatic phrase for "whether he will or no":
velit nolit.
Nay, God Himself will not save men against their wills.
Numquam. Deus Ipse non contra eorum voluntatem salvat homines.
That's grammatically correct. However the word choice isn't the best. I would suggest
immo nec Deus ipse homines salvat invitos.