Help -English to Latin Translation

"Healing the nation's warrior/s" - "Curatio populus proeliator"

Curatio is a noun; you want the participle curans (if singular) or curantes
(if plural).
I'd use respublica rather than populus. In either case, use the genetive --
rei publicae or populi.
Proeliator should be accusative plural -- proeliatores.

So...
Curans proeliatores populi.


"Combat strength through health" -"Certamen vires per valetudo"
I assume you mean "combat" as an adjective to describe strength (i.e. the strength required for combat). Otherwsise, it sounds as if your mission is to fight strength by means of health.

Certamen is a noun; in this case I'd advise a gerund phrase such as ad
pugnandum (for fighting).

Valetudo should be accustaive (object of the preposition per) --
valetudinem.

So...

Vires ad pugnandum per valitudinem.

Thanks George.

You're welcome, Cheryl.