1)The tired farmers quench the thirst.
Sitim sedant fessi agricolae
2)Antonio wished Rome and Napoli.
Romam et Neapolim Antonio desiderabat
3)Many times the soldiers are troubled by hunger by thirst.
Saepe vexantur sede et fame miletes
4)The diseases are harmful to the stregthens of the body.
Corporis viribus morbi noxii sunt
5)Great was the honor of the optimates.
Optimatum honor magnus fuit
6)The veterans set up the strengthen of the roman armies.
Robur exercituum romani veteranus sunt
7)The moviments of the body are advantageous to the members.
Corporis motus artibus commodus sunt
I am home.
Domi sum
9) The return of spring cheers up the farmers
Veris reditus agricolas delectat.
10)History explains the things and the cause of the things.
Historia res et rerum causam explicat
1)The tired farmers quench the thirst.
Sitim sedant fessi agricolae
Seems OK. Although the more normal word order would be “agricolae fessi sitim sedant”, and of course you’re using the unusual form of sitis, -is. Sitem might be more appropriate.
2)Antonio wished Rome and Napoli.
Romam et Neapolim Antonio desiderabat
Antonius is the Roman name. I don’t understand the English here.
3)Many times the soldiers are troubled by hunger by thirst.
Saepe vexantur sede et fame miletes
4)The diseases are harmful to the stregthens of the body.
Corporis viribus morbi noxii sunt
To be harmful is usually noceo, nocere. Takes dative object.
Morbi viribus corporis nocent.
3 seems OK.
5)Great was the honor of the optimates.
Optimatum honor magnus fuit
6)The veterans set up the strengthen of the roman armies.
Robur exercituum romani veteranus sunt
Robur means “strength, best part, elite” doesn’t it?
Veterani is the plural form - best use that.
Roman arm_ies_ is exercituum romanorum.
I think some kind of predicative dative construction might be called for here…
7)The moviments of the body are advantageous to the members.
Corporis motus artibus commodus sunt
Cool I am home.
Domi sum
With 7 I probably would use a predicative dative (aka a double dative). Motus corporis usui artibus sunt.
Domi sum means as you so correctly say “I am at home”
- The return of spring cheers up the farmers
Veris reditus agricolas delectat.
10)History explains the things and the cause of the things.
Historia res et rerum causam explicat
10 is good.
9 also.
This exercises are taken from a Brazilian or Portuguese textbook, yes?
Several times I’ve wondered what the meaning of the phrase to be translated into Latin is. For example, the legs and arms in English are refered to as limbs. Members are the kinds of things clubs and trade unions have. Still, I think your English is superb.
If you find real difficulty you might try your luck asking in Portuguese. There are some here who claim some facility with that language.
1)The tired farmers quench the thirst.
Sitim sedant fessi agricolae
sitis is one of the handful of pure i-stems which preserve the -im accusative, so sitim is probably better than sitem.
2)Antonio wished Rome and Napoli.
Romam et Neapolim Antonio desiderabat
If Napoli is the Latin nominative, the accusative should be Napolos (2nd decl. plur. masc.).
3)Many times the soldiers are troubled by hunger by thirst.
Saepe vexantur sede et fame miletes
the stem of miles is milit-.
4)The diseases are harmful to the stregthens of the body.
Corporis viribus morbi noxii sunt
I think you mean “strengths”.
7)The moviments of the body are advantageous to the members.
Corporis motus artibus commodus suntWith 7 I probably would use a predicative dative (aka a double dative). Motus corporis usui artibus sunt.
Why not use utor, uti in the present?
Quote:
2)Antonio wished Rome and Napoli.
Romam et Neapolim Antonio desiderabat
If Napoli is the Latin nominative, the accusative should be Napolos (2nd decl. plur. masc.).
Neapolis, -is (f.)
Do you mean Antonius wants Rome and Naples?
That would be: Antonius Romam Neapolimque (-em?) desiderabat.
Neapolis = new city in Greek. But I’m sure you knew that 
Ah, thanks for that. I would think the accusative would be Neapolem then, but since it is Greek I am unsure.