For the first one, you could also go with mundus for "mankind", since homines generally refers to a large group of people as opposed to an entity.
EDIT: Evolvant comes from evolvo, which is a third conjugation verb. Thus, evolvant is in the subjunctive mood as opposed to the indicative, evolvunt, which you should be using here.
Evolvo means "roll out" or "unfold", so I think adveniunt ("arrive at" or "reach"), or augescunt ("grow" or prosper" may better suit your translation. It all depends on the specific type of "evolution" you are talking about (ex: intellectual, physical, etc).
Also note that if you choose to go with mundus, you need a singular ending (-t) on the verb.
The second one looks good!
In the third phrase, alternate translations for "reason" are mens and argumentum, but ratio is perfectly acceptable too.
EDIT: Again, mind the conjugation. Refellat is the 3rd person active subjunctive of the word refello, so you should use refellit instead.
EDIT: Just a general note about verb conjugations:
Conjugations are determined by looking at the 2nd principal part of the verb.
1st conjugation verbs end with -āre.
amō, amāre, amāvī, amātum = love, like
dō, dāre, dedī, datum = give
2nd conjugation verbs end with -ēre.
videō, vidēre, vidī, visum = see, look at
doceō, docēre, docuī, doctum = to teach
3rd conjugation verbs end with -ere.
dicō, dicere, dixī, dictum = say, speak
cadō, cadere, cecidī, casum = fall
4th conjugation verbs end with -īre.
dormiō, dormīre, dormīvī, dormītum = sleep, rest
veniō, venīre, venī, ventum = come
The present stem of a verb is found by dropping the -re from the 2nd principal part for 1st and 2nd conjugation verbs, and by dropping the -ō from the 1st principal part for 3rd and 4th conjugation verbs. Once you obtain the stem, you can then add on the appropriate endings.
Hope this was helpful!