Medica quoque quietem et aquam tepidam commendat, ut puella melius valeat.

Medica is the feminine form of the noun, meaning female doctor or woman physician.
Medicus would be masculine.

So the sentence tells us that the doctor is a woman.

Quoque means also or too.

In Latin, quoque often comes after the word it is closely connected with. Here, medica quoque means the doctor also.

So the idea is that the doctor, in addition to something already mentioned, recommends these things.

They are in the accusative because they are the direct objects of commendat.

The verb commendat means recommends, and the doctor is recommending:

• quietem = rest
• aquam tepidam = warm/lukewarm water

So they are the things being recommended.

Because the phrase is a direct object, both words must be in the accusative singular feminine:

• aqua → aquam
• tepida → tepidam

The adjective tepidam must agree with aquam in:

• gender: feminine
• number: singular
• case: accusative

That is normal Latin adjective agreement.

Tepidam means warm, lukewarm, or tepid.

It usually does not mean very hot.
So aquam tepidam is warm water or lukewarm water.

Here ut introduces a purpose clause.

It means so that or in order that.

So:

• ut puella melius valeat = so that the girl may be better / so that the girl may recover more fully

The doctor recommends rest and warm water for a purpose: the girl's improved health.

Because it is in an ut-purpose clause.

A purpose clause in Latin normally uses:

• ut
  • subjunctive

So valeat is subjunctive because the clause expresses the goal or intention behind the recommendation.

Valeat is:

• from valeo, valere = to be strong, be well, be healthy
• 3rd person singular
• present subjunctive active

So valeat means something like:

• may be well
• may get better
• may recover

The exact English wording depends on context.

Because melius is an adverb here, not an adjective.

It modifies the verb valeat:

• valeat = be well
• melius valeat = be better, feel better, recover better

By contrast, melior is an adjective meaning better and would describe a noun, not a verb.

Because puella is the subject of valeat in the subordinate clause.

In ut puella melius valeat, the girl is the one who is supposed to become better. So puella must be nominative.

It is related, but in this context commendat is best understood as recommends.

Latin commendare can mean things like:

• entrust
• commend
• recommend
• advise

Here recommends fits the medical context best.

Because this is not a content clause like she recommends that the girl... in English.
Instead, Latin uses a purpose clause:

• commendat ... ut puella melius valeat
• she recommends ... so that the girl may get better

Latin is focusing on the purpose of the treatment, not simply reporting a recommendation with a that-clause.

Yes, the word order is perfectly normal for Latin.

Latin word order is more flexible than English because the endings show the grammatical relationships. This allows Latin to place words for emphasis or style.

Here the structure is clear:

• Medica quoque = the doctor also
• quietem et aquam tepidam commendat = recommends rest and warm water
• ut puella melius valeat = so that the girl may feel better

The important thing is to follow the endings and the clause structure, not to expect strict English-style word order.

Yes. Depending on how natural you want the English to sound, you might translate it as:

• so that the girl may feel better
• so that the girl may get better
• in order that the girl may recover more quickly
• so that the girl will be better

The Latin grammar is the same; the English wording can vary a little depending on context.