Mater pulvinum sub capite pueri ponit, quo commodius dormiat.

Yes:

• Mater — nominative singular, the mother; the subject.
• pulvinum — accusative singular, pillow/cushion; the direct object.
• sub — preposition, under.
• capite — ablative singular of caput, head.
• pueri — genitive singular of puer, of the boy.
• ponit — 3rd person singular present active indicative of pono, places / puts.
• quo — here an adverbial word introducing a purpose clause, especially with a comparative.
• commodius — comparative adverb, more comfortably / more conveniently.
• dormiat — 3rd person singular present active subjunctive of dormio, may sleep.

So the structure is:

• main clause: Mater pulvinum sub capite pueri ponit
• purpose clause: quo commodius dormiat

Because it is the direct object of ponit.

The mother is doing the action of placing, and the thing being placed is the pillow, so Latin puts pulvinum in the accusative.

• mater = the one who acts
• ponit = places
• pulvinum = the thing placed

Because capite is ablative, and with sub the ablative commonly expresses position: under the head.

A helpful basic rule is:

• sub + accusative = motion to a position under something
• sub + ablative = location under something

Here the idea is the pillow’s resulting position: it is under the boy’s head.

A learner may notice that the verb ponit involves movement, so an accusative might seem possible. That is a fair question. But Latin often uses the ablative here when the emphasis is on the place where the object ends up lying.

Because it means of the boy and depends on capite.

So:

• capite pueri = the head of the boy = the boy’s head

This is a very common use of the genitive: showing possession or close relationship.

Here quo means something like so that, in order that, or more literally by which / whereby.

In this sentence it introduces a purpose clause. It is especially common when the clause contains a comparative word such as commodius.

So:

• quo commodius dormiat = so that he may sleep more comfortably

Not in a simple one-to-one way like the pillow which.

Historically, quo is related to the relative pronoun, so its original force is something like by which or whereby. But in this kind of sentence it functions as a standard way to introduce a purpose clause, especially with a comparative.

So a beginner should understand it mainly as:

• quo + comparative + subjunctive = so that ... more ...

Because the idea is more comfortably, not just comfortably.

The mother places the pillow under the boy’s head in order that he may sleep more comfortably than he otherwise would.

Also, commodius is an adverb, because it modifies the verb dormiat:

• not a more comfortable boy
• but sleep more comfortably

Latin comparative adverbs often end in -ius, as here.

Because it is in a purpose clause.

Latin uses the subjunctive after ut or, in this special pattern, quo, to express purpose:

• The mother places the pillow ... so that he may sleep more comfortably.

So dormiat is not subjunctive because the action is doubtful; it is subjunctive because the clause expresses the intended result/purpose of the mother’s action.

It is present subjunctive because the main verb ponit is present, so Latin uses the present subjunctive in the subordinate clause.

The subject is the boy, understood from the context.

Latin often leaves subject pronouns unstated when they are clear. The verb ending -at tells you the subject is he/she/it in the 3rd person singular, and the context shows that it is the boy who is meant:

• the mother puts the pillow under the boy’s head
• so that he may sleep more comfortably

Latin does not need to say is or ille here.

Because quo + comparative + subjunctive is a standard and very common Latin construction.

When a purpose clause contains a comparative word such as:

• commodius = more comfortably
• facilius = more easily
• celerius = more quickly

Latin often prefers quo rather than ut.

So this pattern is worth remembering as a set:

• quo + comparative + subjunctive

meaning:

• so that ... more ...

Yes, but it is also very normal Latin.

Latin word order is more flexible than English because the case endings show each word’s function. This sentence has a natural flow:

• Mater — topic/subject first
• pulvinum — the object
• sub capite pueri — where the pillow is placed
• ponit — the main verb at the end of the clause
• quo commodius dormiat — the purpose clause after that

A very literal English-style order would sound less natural in Latin. The given word order is clear and idiomatic.