Meine Tochter sitzt gern auf der Schaukel und singt leise.

Because Tochter is a feminine noun in German.

• mein = my (used with some masculine or neuter forms)
• meine = my (used here with a feminine noun in the nominative singular)

So:

• mein Sohn = my son
• meine Tochter = my daughter

In this sentence, Tochter is the subject, so it is in the nominative case.

It can mean either, depending on context.

German present tense often covers both:

• she sits
• she is sitting

So Meine Tochter sitzt ... can mean:

• My daughter sits ...
• My daughter is sitting ...

In natural English, is sitting is often the more likely translation in a sentence like this, but grammatically German just uses the normal present tense.

Gern means gladly, with pleasure, or more naturally in English, likes to when used with a verb.

So:

• Meine Tochter sitzt gern auf der Schaukel = My daughter likes sitting on the swing / My daughter enjoys sitting on the swing

German often places gern after the conjugated verb:

• Ich lese gern. = I like reading.
• Er singt gern. = He likes singing.

So sitzt gern is a very normal word order.

Because this sentence describes a location, not a movement toward a destination.

The preposition auf can take two cases:

• dative for location: on, on top of, at
• accusative for movement toward something

Here, the daughter is already on the swing, so German uses the dative:

• auf der Schaukel = on the swing

Compare:

• Sie sitzt auf der Schaukel. = She is sitting on the swing.
• Sie setzt sich auf die Schaukel. = She sits down onto the swing.

That is a very common German pattern with so-called two-way prepositions.

Because der here is not nominative feminine. It is dative feminine.

The noun die Schaukel is feminine, and its article changes by case:

• nominative: die Schaukel
• accusative: die Schaukel
• dative: der Schaukel
• genitive: der Schaukel

So in auf der Schaukel, der shows that Schaukel is feminine singular in the dative case.

Yes. In this sentence, Schaukel means swing, usually the kind found in a playground or garden.

So:

• auf der Schaukel = on the swing

The word can also relate more generally to something that swings, but swing is exactly the right translation here.

Because the subject stays the same: Meine Tochter.

In German, just as in English, you do not need to repeat the subject if two verbs are connected and the subject is unchanged.

So:

• Meine Tochter sitzt gern auf der Schaukel und singt leise.

means:

• My daughter likes sitting on the swing and sings softly.

If you repeated the subject, it would still be grammatical, but less natural here:

• Meine Tochter sitzt gern auf der Schaukel und meine Tochter singt leise.

That sounds unnecessarily repetitive.

It is not actually at the very end of a full clause in an unusual way — it is in the normal position for a main clause after und.

German main clauses usually place the conjugated verb in second position. After und, the second clause is also a main clause, and the subject is omitted because it is understood.

So the structure is roughly:

• Meine Tochter | sitzt | gern auf der Schaukel
• (meine Tochter) | singt | leise

Since the subject is omitted in the second clause, singt comes directly after und:

• ... und singt leise

That is completely normal.

Leise means softly or quietly here.

It comes from an adjective meaning quiet/soft, but in this sentence it functions as an adverb, describing how she sings.

• leise singen = to sing softly/quietly

German often uses the same form for adjectives and adverbs:

• ein leises Lied = a quiet/soft song
• Sie singt leise. = She sings softly.

Unlike English, German usually does not add a special ending like -ly to form adverbs.

Yes. Gern and gerne mean the same thing.

• Ich lese gern.
• Ich lese gerne.

Both mean I like reading / I read gladly.

Gern is just a slightly shorter form. In everyday German, both are common.

Yes, that is possible, but it changes the structure and slightly changes the emphasis.

Original:

• Meine Tochter sitzt gern auf der Schaukel und singt leise.

This presents two actions:

1. she likes sitting on the swing
2. she sings softly

Alternative:

• Meine Tochter singt leise auf der Schaukel.

This focuses more directly on the singing and simply says where she is singing: on the swing.

So both are grammatical, but they do not highlight exactly the same thing.

Usually it means likes to sit on the swing or enjoys sitting on the swing.

That is the most important use of gern with a verb: it expresses liking or enjoyment.

So:

• Sie sitzt gern auf der Schaukel.
  = She likes sitting on the swing.

It is less about her emotional expression in that moment and more about the fact that she enjoys that activity.

Schaukel is pronounced roughly like SHOW-kel.

A few pronunciation notes:

• sch sounds like English sh
• au sounds like the ow in now
• the el at the end is light, roughly like -el in tunnel, though not exactly the same

A rough English-friendly guide is:

• SHAU-kel or SHOW-kel

The stress is on the first syllable: SCHAU-kel.

You can understand it word for word, but a fully natural English translation may need adjustment.

Word by word:

• Meine = my
• Tochter = daughter
• sitzt = sits / is sitting
• gern = gladly / likes to
• auf der Schaukel = on the swing
• und = and
• singt = sings / is singing
• leise = softly / quietly

A very literal translation might be:

• My daughter sits gladly on the swing and sings softly.

That is understandable, but more natural English would usually be something like:

• My daughter likes sitting on the swing and sings softly.
• My daughter is sitting on the swing and singing softly.

Which English version is best depends on the context.