Der Arzt verbindet meinen Daumen, weil er noch weh tut.

In this sentence, verbinden means to bandage, to dress a wound, or to put a bandage on.

So:

• Der Arzt verbindet meinen Daumen = The doctor bandages my thumb / The doctor dresses my thumb

You are right that verbinden can also mean to connect in other contexts. German verbs often have more than one meaning, and the context tells you which one is meant.

For example:

• zwei Städte verbinden = to connect two cities
• eine Wunde verbinden = to bandage a wound

Here, because the subject is the doctor and the object is my thumb, the medical meaning is the natural one.

Because meinen Daumen is the direct object of the verb verbindet.

The doctor is doing something to the thumb, so my thumb is in the accusative case.

• nominative: mein Daumen = my thumb
• accusative: meinen Daumen = my thumb as a direct object

Since Daumen is a masculine noun (der Daumen), mein changes in the accusative:

• der Daumen
• mein Daumen
• meinen Daumen after a verb that takes a direct object

So:

• Mein Daumen tut weh. = My thumb hurts.
  Here it is the subject, so nominative.
• Der Arzt verbindet meinen Daumen. = The doctor bandages my thumb.
  Here it is the object, so accusative.

Because weil introduces a subordinate clause.

German normally puts a comma before subordinate clauses, especially with words like:

• weil = because
• dass = that
• wenn = if/when
• obwohl = although

So the structure is:

• Der Arzt verbindet meinen Daumen, weil ...

That comma is required in standard written German.

Because weil sends the conjugated verb to the end of the clause.

In a normal main clause, German uses verb-second word order:

• Er tut noch weh.

But after weil, the clause becomes subordinate, and the verb goes to the end:

• ..., weil er noch weh tut.

That is one of the most important word-order patterns in German.

Compare:

• Mein Daumen tut weh.
• ..., weil mein Daumen weh tut.

It is a fixed expression made of weh + tun, and together it means to hurt or to be painful.

You will usually see it split in a main clause:

• Mein Daumen tut weh.

But in a subordinate clause, the conjugated verb goes to the end, so the two parts come together there:

• ..., weil mein Daumen weh tut.

So it behaves a bit like a separable expression in terms of word order, even though learners often just memorize weh tun as a unit meaning to hurt.

A very useful pattern is:

• Etwas tut weh. = Something hurts.
• Mein Arm tut weh. = My arm hurts.
• Der Zahn tut weh. = The tooth hurts.

Here er refers to der Daumen.

So:

• weil er noch weh tut = because it still hurts

This can confuse English speakers for two reasons:

1. er usually means he, but in German it can also refer to a masculine noun that would be it in English.
2. Both der Arzt and der Daumen are grammatically masculine, so grammar alone does not fully disambiguate it.

In this sentence, context makes it clear that the thumb is the thing that still hurts, not the doctor.

So English translates er here as it, not he.

Because German pronouns follow grammatical gender, not natural gender the way English usually does.

• der Daumen is masculine
• so the matching pronoun is er

In English, body parts are usually it, but in German they take the pronoun that matches the noun’s gender:

• der Daumen → er
• die Hand → sie
• das Bein → es

Examples:

• Wo ist der Stift? Er ist hier. = Where is the pen? It is here.
• Wo ist die Tasche? Sie ist hier. = Where is the bag? It is here.
• Wo ist das Buch? Es ist hier. = Where is the book? It is here.

So er does not automatically mean a male person.

Here noch means still.

So:

• weil er noch weh tut = because it still hurts

It shows that the pain is continuing.

Compare:

• Er tut weh. = It hurts.
• Er tut noch weh. = It still hurts.

So noch adds the idea that the problem has not gone away yet.

Yes, absolutely.

Both are correct:

• Der Arzt verbindet meinen Daumen, weil er noch weh tut.
• Der Arzt verbindet meinen Daumen, weil mein Daumen noch weh tut.

Using mein Daumen again makes the sentence more explicit and avoids any possible ambiguity. Using er sounds more natural if the referent is already clear from context.

So the choice is mostly about style and clarity, not grammar.

German often uses articles where English may omit them.

• Der Arzt = the doctor

In a normal sentence like this, using the article is expected. Without it, Arzt would sound incomplete unless it were part of a special structure, such as a title or form of address.

So:

• Der Arzt verbindet meinen Daumen. = normal statement
• Arzt! = calling out Doctor!

In ordinary descriptions, German usually wants the article with nouns like this.

Because all nouns are capitalized in German.

So in this sentence:

• der Arzt
• mein Daumen

Both Arzt and Daumen are nouns, so they begin with a capital letter.

This is one of the most visible differences between German and English spelling. It applies to all nouns, not just proper names.