Learn Hardcore German: Die Bäuerin füttert die Schafe, während ihr Mann den Traktor repariert. - The female farmer feeds the sheep while her husband repairs the tractor.

In German, all nouns are capitalized, no matter where they appear in the sentence.
Bäuerin is a noun (meaning female farmer), so it must begin with a capital letter.

What is the difference between Bauer and Bäuerin?

Bauer = male farmer (masculine noun)
Bäuerin = female farmer (feminine noun)

Many professions form the feminine version with -in:

Lehrer → Lehrerin (teacher)
Arzt → Ärztin (doctor)

The äu in Bäuerin is just the way the word is formed from Bauer; you’re not free to choose spelling here – you simply have to learn Bäuerin as the correct feminine form.

What cases are the different noun phrases in?

Die Bäuerin – nominative singular (subject of the main clause: who is feeding?)
die Schafe – accusative plural (direct object in the main clause: whom/what is she feeding?)
ihr Mann – nominative singular (subject of the subordinate clause: who is repairing?)
den Traktor – accusative singular (direct object in the subordinate clause: what is he repairing?)

Why is it den Traktor and not der Traktor?

Traktor is a masculine noun.

The definite article for masculine singular changes with case:

Nominative: der Traktor (subject)
Accusative: den Traktor (direct object)

Here, den Traktor is the direct object of repariert, so it takes the accusative, which is den.

Why is it die Schafe and not something like die Schafen?

The singular is:

das Schaf (neuter)

The plural is:

die Schafe

For all plural nouns, the definite article in the nominative and accusative is die, regardless of gender:

die Schafe (plural nominative or accusative)
die Hunde
die Frauen

There is no extra -n on Schafe in the accusative; the form Schafen would be dative plural, which you don’t need here.

Why does füttert come in second position, but repariert goes to the end?

German has two different clause types here:

Main clause:
Die Bäuerin füttert die Schafe
In a main clause, the conjugated verb is in second position → füttert is the second element.
Subordinate clause introduced by während:
während ihr Mann den Traktor repariert
während is a subordinating conjunction, so in this clause the conjugated verb goes to the end → repariert is at the end of the clause.

So:

Main clause: verb in 2nd position.
Subordinate clause (with während): verb at the end.

What kind of word is während, and what does it do to word order?

während is a subordinating conjunction meaning while.

Subordinating conjunctions introduce a dependent (subordinate) clause and send the conjugated verb to the end of that clause:

…, während ihr Mann den Traktor repariert.
…, weil es regnet. (because it is raining)
…, dass er müde ist. (that he is tired)

So während both links the two actions in time (at the same time) and triggers verb-final word order in its clause.

Can I put the während-clause first?

Yes. You can say:

Während ihr Mann den Traktor repariert, füttert die Bäuerin die Schafe.

Rules then:

In the subordinate clause with während, the verb repariert stays at the end.
After that clause and the comma, the following main clause still keeps verb in second position.
Here, the whole subordinate clause counts as position 1, so:
- Position 1: Während ihr Mann den Traktor repariert
- Position 2: füttert (the finite verb of the main clause)

Why is it ihr Mann and how do I know it means her husband?

ihr is a possessive pronoun. It can mean:

her (belonging to she)
their
your (formal, addressing one female person: Ihr)

In this sentence, the most natural reading is:

ihr Mann = her husband, referring back to die Bäuerin (a woman).

German often uses context to decide which meaning of ihr is intended. Since the only clear possessor introduced before is die Bäuerin (a female person), ihr Mann is understood as the farmer woman’s husband.

Why is it ihr Mann and not ihren Mann?

The form of the possessive changes with the case of the noun it modifies.

Here, Mann is the subject of the subordinate clause (who is repairing? → ihr Mann), so it is in the nominative case.

For masculine singular nominative, the possessive pronoun ihr has no extra ending:

Nominative: ihr Mann
Accusative: ihren Mann (She sees her husband → Sie sieht ihren Mann)

So ihr Mann is correct because Mann is nominative.

Why is there a comma before während?

In German, subordinate clauses must be separated by a comma from the main clause.

Die Bäuerin füttert die Schafe, während ihr Mann den Traktor repariert.

The part starting with während is a separate clause, so the comma is required, not optional.

Why is the tense simply present (füttert, repariert) even though in English I might say “is feeding / is repairing”?

German Präsens (present tense) covers both:

English simple present (she feeds) and
English present progressive (she is feeding).

So:

Die Bäuerin füttert die Schafe
can mean either The farmer (woman) feeds the sheep (general habit) or
The farmer (woman) is feeding the sheep (right now), depending on context.

The same with repariert (repairs / is repairing). German usually does not need a special progressive form.