Mater genas infantis tangit, sed palma medicae frontem frigidiorem sentit.

Because genas is accusative plural of gena, -ae, meaning cheek. It is the direct object of tangit, so the sentence says that the mother touches the cheeks.

For a first-declension noun:

• nominative singular: gena
• accusative singular: genam
• accusative plural: genas

Because infantis is genitive singular of infans, infantis and means of the baby/child. It shows possession or close association: the baby's cheeks.

If the sentence had infantem, that would be accusative singular, which would make the baby itself the direct object.

Mater is nominative singular, the subject of tangit.

It comes from mater, matris, a third-declension noun. Third-declension nominatives often do not have a very obvious ending, so mater may look less familiar at first than nouns like puella or servus.

It means the doctor's palm or more literally the palm of the doctor.

• palma is nominative singular, the subject of sentit
• medicae is genitive singular, dependent on palma

So this phrase works the same way as genas infantis:

• genas infantis = the baby's cheeks
• palma medicae = the doctor's palm

Yes. Medica is a feminine noun, so medicae here means of the female doctor.

If the doctor were explicitly male, you would normally expect medici from medicus.

By form alone, yes. Medicae could be:

• genitive singular
• dative singular
• nominative plural
• vocative plural

But in this sentence, genitive singular is the natural reading, because it fits with palma: the palm of the doctor.

Because frontem is the direct object of sentit, and frigidiorem describes frontem.

• frontem = accusative singular of frons, frontis
• frigidiorem = accusative singular feminine comparative of frigidus

Latin adjectives agree with the nouns they describe in:

• gender
• number
• case

So frigidiorem must match frontem.

Formally, frigidiorem means colder.

But Latin comparatives do not always need an explicit than ... phrase. Depending on context, it can suggest:

• colder than normal
• colder than before
• rather cold
• unusually cool

So the sentence may be implying that the doctor notices an abnormal temperature.

Because the two verbs focus on different ideas:

• tangit = touches
  This emphasizes the act of making contact.

• sentit = feels / perceives
  This emphasizes the sensation detected through touch.

So the first clause tells you what the mother does, while the second tells you what the doctor's hand perceives.

Yes. Latin can make a body part the grammatical subject when that is the most vivid or natural way to express the idea.

So palma medicae ... sentit means that the doctor feels something with her palm, but Latin lets the palm itself stand as the subject.

English can do something similar in sentences like my hand feels something cold, though Latin often uses this kind of phrasing more freely.

Latin word order is much freer because the endings show the grammatical role of each word.

This sentence uses word order for emphasis and flow:

• Mater comes first to introduce the first subject
• genas infantis stays together as a noun phrase
• sed marks the contrast
• palma medicae introduces the second subject
• frontem frigidiorem keeps the noun and its adjective together before the verb
• tangit and sentit stand at the ends of their clauses, which is very common in Latin

So the order is not random; it is stylistic rather than strictly English-like.

Because Classical Latin has no articles.

A noun like mater can mean:

• the mother
• a mother
• sometimes simply mother

The same is true for the other nouns in the sentence. English has to add articles, but Latin leaves that to context.

No. Infans, infantis is a common-gender noun, so it can refer to either a male or a female child. The form infantis does not tell you the sex.

Only the context would make that clear.