Ell vol parlar amb la professora després de la classe.

Yes. Catalan often drops subject pronouns when the subject is clear from the verb form.

So you could say:

• Vol parlar amb la professora després de la classe.

and it would still mean the same thing.

Ell is included here for emphasis, contrast, or clarity. For example, it can help if you want to stress he as opposed to someone else.

The verb here is voler (to want). Its he/she form in the present tense is vol.

So:

• ell vol = he wants

Catalan commonly uses voler + infinitive directly:

• vol parlar = wants to speak

There is no extra preposition like a in this structure.

Parlar is the infinitive form of the verb, meaning to speak or to talk.

After vol (wants), Catalan uses the infinitive:

• vol parlar
• vol menjar
• vol estudiar

This is very similar to English wants to speak, except Catalan does not use a separate word for to here.

Here, amb means with, and it is the normal preposition used after parlar when you mean to speak with someone.

So:

• parlar amb algú = to speak with someone

This is one of the standard patterns you should learn as a chunk:

• parlar amb la professora
• parlar amb els amics
• parlar amb mi

In some contexts, speakers may also use parlar a algú for speak to someone, but parlar amb is extremely common and natural.

Catalan often uses the definite article more than English does.

So where English might say:

• the teacher

Catalan says:

• la professora

In many contexts, Catalan prefers the article before professions or known people in a situation. Here it sounds natural because it refers to a specific teacher.

Also note:

• professora = female teacher
• professor = male teacher

Because després normally combines with de before a noun.

So the pattern is:

• després de + noun
• després de la classe = after class

Examples:

• després de dinar = after lunch / after eating lunch
• després de la feina = after work

You should learn després de as a fixed expression.

Because classe is a feminine singular noun, so it takes the article la.

• la classe = the class

After de, the article stays separate here:

• de la classe

Compare this with masculine singular nouns beginning with a normal consonant:

• del llibre = de + el llibre

But with feminine singular:

• de la classe

There is no contraction with la.

It usually means class in the sense of a lesson or teaching session.

So in this sentence, després de la classe most naturally means after the class / after class.

Depending on context, classe can have related meanings, but here the most natural interpretation is the lesson or period of teaching, not the physical classroom.

The given order is very natural:

• Ell vol parlar amb la professora després de la classe.

But Catalan can move elements around for emphasis or style. For example:

• Després de la classe, ell vol parlar amb la professora.

This puts more focus on when.

The basic sentence is still standard subject + verb + infinitive + complement + time expression, but Catalan has some flexibility.

Because its position and meaning make it function as a time expression for the action:

• He wants to speak with the teacher after class.

It tells us when he wants to speak, not which teacher.

If it modified la professora, the meaning would be strange, as if there were some special teacher after class. So context and normal sentence structure make the intended reading clear.

Usually, if ell is included, it is not heavily stressed unless you want contrast.

For example:

• Ell vol parlar... = neutral, just stating the subject
• ELL vol parlar, no ella. = emphatic contrast

Because Catalan often omits subject pronouns, including one can already add a bit of emphasis or clarity, even without heavy stress.

Yes. Professora is grammatically and semantically feminine, so it refers to a female teacher.

If the teacher were male, you would say:

• el professor

So this sentence specifically refers to speaking with a female teacher.

In standard Catalan, no. You normally need després de before a noun phrase:

• després de la classe

Leaving out de would be ungrammatical in standard usage.

English allows after class without an article in many cases, but Catalan usually keeps the fuller structure here.