Над парком появилась радуга, хотя одна туча ещё висела над рекой.

Because the preposition над usually takes the instrumental when it means above / over in a location sense.

So:

• над парком = over the park
• над рекой = over the river

This is a very common pattern:

• над домом = above the house
• над городом = over the city
• над морем = over the sea

So in this sentence, both phrases are describing location, and that is why the nouns after над are instrumental.

Because the subject is радуга, and радуга is a feminine singular noun.

In the past tense, Russian verbs agree with the subject in gender and number:

• masculine: появился
• feminine: появилась
• neuter: появилось
• plural: появились

Since радуга is feminine, the verb must be появилась.

Because радуга is the subject of the verb появилась.

The sentence is basically:

• радуга появилась = a rainbow appeared

The thing doing the action of appearing is the rainbow, so it stays in the nominative.

Russian word order is much more flexible than English word order. Both are possible:

• Радуга появилась над парком
• Над парком появилась радуга

The version in your sentence sounds natural because it first sets the scene:

• Над парком = where?
• появилась радуга = what happened there?

This kind of order is very common in Russian. English usually needs a more fixed order, but Russian can move parts around for focus and style.

Появилась means appeared or came into view.

The verb is появиться, which is perfective. That means it presents the action as a completed event: the rainbow came into existence / became visible.

So the sentence is not describing the rainbow as simply existing in the sky; it is describing the moment it appeared.

Compare:

• появилась = appeared
• была = was
• была видна = was visible

In Russian, висеть literally means to hang, but it is also commonly used for things suspended in the air or seeming to stay in one place above something.

So:

• туча висела над рекой literally = a cloud was hanging over the river

In natural English, we might say:

• a cloud still hung over the river
• a cloud was still over the river

Russian often uses висеть for clouds, fog, smoke, and similar things in the air.

Because here the sentence describes an ongoing state, not a completed action.

• висела is imperfective: it tells us the cloud was hanging / remained hanging
• повисела would mean something more like hung for a while, which does not fit as well here

The contrast in the sentence is important:

• the rainbow appeared — a completed event
• the cloud was still hanging — an ongoing situation

So появилась + висела is a very natural aspect pairing.

Хотя means although, though, or even though.

It introduces a clause that contrasts with the main clause:

• Над парком появилась радуга = A rainbow appeared over the park
• хотя одна туча ещё висела над рекой = although one cloud was still hanging over the river

So the idea is: a rainbow appeared despite the fact that there was still a cloud over the river.

Because хотя introduces a subordinate clause, and Russian normally separates such clauses with a comma.

So:

• main clause: Над парком появилась радуга
• subordinate clause: хотя одна туча ещё висела над рекой

Russian punctuation is quite strict about this kind of clause boundary, so the comma is required.

Yes, одна is the feminine form of one, because туча is feminine.

Here одна туча can mean simply:

• one cloud

But in context it can also have a slight nuance of:

• a single cloud
• just one cloud

That can make the contrast stronger: a rainbow appeared, even though one cloud was still there.

Forms of one:

• один for masculine
• одна for feminine
• одно for neuter

Both relate to clouds, but they are not the same.

• облако = cloud, neutral/general word
• туча = dark cloud, storm cloud, rain cloud

So туча is stronger and more dramatic. It suggests bad weather or a heavy dark cloud, which fits well with the contrast: a rainbow appeared even though a storm cloud was still hanging over the river.

Here ещё means still.

So:

• ещё висела = was still hanging

In other contexts, ещё can also mean:

• more
• else
• again
• sometimes yet

But in this sentence, the meaning is clearly still.

Yes. Russian allows that too:

• Хотя одна туча ещё висела над рекой, над парком появилась радуга.

This means the same thing. The difference is mainly one of emphasis and flow.

• Original sentence: first tells you about the rainbow, then adds the contrast
• Reordered sentence: first presents the obstacle/background, then gives the main event

Both are correct and natural.

Not always. Над often corresponds to above, over, or sometimes overhead, depending on context.

In this sentence:

• над парком is best translated as over the park
• над рекой is also most naturally over the river

So над does not map to just one English word. The core idea is position higher than something, often directly over it.

Yes. The sentence uses two different kinds of past meaning:

• появилась = a completed event in the past
• висела = an ongoing state in the past

That creates a very natural contrast:

• something new happened: the rainbow appeared
• while something else was still continuing: the cloud was still hanging there

English often expresses the same contrast with simple past plus still, or with past continuous depending on style. Russian does it through verb choice and aspect.