Medicul apasă compresa.

They are:

medic = doctor
a apăsa = to press
compresă = compress / pad

In the sentence, medicul and compresa are inflected noun forms, and apasă is a conjugated verb form.

Because -ul is the Romanian definite article for many masculine singular nouns.

So:

medic = a doctor / doctor
medicul = the doctor

Unlike English, Romanian usually puts the at the end of the noun instead of using a separate word.

Compresă is the basic, indefinite form: a compress / a pad.

When it becomes definite, Romanian adds the article to the end:

compresă → compresa = the compress / the pad

So the final -ă changes to -a in the definite singular form.

Apasă is the 3rd person singular present tense of a apăsa.

That means it corresponds to:

he presses / she presses / it presses

Since the subject here is medicul, the full meaning is the doctor presses.

Because a apăsa is the infinitive, the form meaning to press. In a normal sentence, Romanian uses a conjugated form, not the infinitive.

So:

a apăsa = to press
apasă = he/she presses

This is completely normal. Romanian verbs change form depending on person, number, and tense.

Romanian often leaves subject pronouns out when they are not needed. The verb ending already shows the person and number, and here the subject is also stated explicitly as medicul.

So Romanian does not need to say:

El apasă compresa

unless there is a special reason to emphasize he.

In this sentence, the normal word order is:

subject + verb + object

So:

Medicul = the subject, the one doing the action
apasă = the verb
compresa = the direct object, the thing being pressed

Romanian can sometimes change word order for emphasis, but this sentence uses the most straightforward pattern.

Sometimes, yes, but the basic order here is the most neutral one: Medicul apasă compresa.

If you simply swap the nouns and say Compresa apasă medicul, it would normally mean The compress presses the doctor, which changes the meaning.

So for a learner, it is safest to treat this sentence as a standard subject-verb-object structure.

Yes, they are different sounds.

ă is a short central vowel, somewhat like the vowel in the English a of about.
Plain a is a clearer ah sound.

So:

apasă ends in ă
compresa ends in plain a

That difference is important in Romanian spelling and pronunciation.

Yes, it matters.

medic is masculine.
compresă is feminine.

Gender affects things like the definite article and adjective agreement. In this sentence you can already see it:

medicul = masculine singular definite
compresa = feminine singular definite

So the endings are not random; they reflect grammatical gender.