There are a number of different ways to say "upside down" in German. As an adverb, you might have seen kopfüber. 

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Das weiß ich. Und sie hängen kopfüber, wenn sie schlafen.

I know that. And they hang upside down when they sleep.

Caption 41, Meine Freundin Conni: Conni schläft im Kindergarten

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Der arme Soldat lag kopfüber im Rinnstein, als es anfing zu regnen.

The poor soldier lay upside down in the gutter as it started to rain.

Caption 32, Märchen - Sagenhaft: Der standhafte Zinnsoldat

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The verbal idiom to know is (etwas) auf den Kopf stellen. 

Ich hab alles verändert und auf den Kopf gestellt.

I've changed everything and turned it upside down.

Caption 16, Christina Stürmer: Ein halbes Leben

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Und steh ich kopf, drehst du mich wieder um

And when I'm upside down, you turn me right side up

Caption 19, Wincent Weiss: Wer wenn nicht wir

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For the phrase "inside out," the context matters. A shirt being worn inside out by accident is verkehrt herum or auf links. But the English idiom of "turning inside out" when looking for something and thereby causing a big mess is better translated as umkrempeln.

Ich glaube, der würde sich in seiner eigenen Halle nicht mehr auskennen, weil die Halle ist einmal komplett umgekrempelt.

I believe, he wouldn't know his way around his own halls, because the hall has been completely turned inside out.

Captions 48-49, Rhein-Main-Ferien: Technische Sammlung Hochhut

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The word "backwards" is, however, quite simple, as rückwärts is the most common translation by far. 

Warum die Zeit vergeht, sich niemals rückwärts dreht.

Why time goes by, never turns backwards.

Caption 5, Es war einmal … Entdecker und Erfinder: Archimedes

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Der Athlet springt rücklings ab und dreht sich danach ebenfalls rückwärts.

The athlete jumps off backwards and afterwards likewise rotates backwards.

Caption 16, Olympische Spiele: Wasserspringen

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Further Learning
You can find more examples on Yabla German.

From bonfires at Christmas markets to a cozy fireplace, winter in Germany is a time to keep warm! Different types of fires have different translations in German.

Der bereitet jetzt schon mal das Lagerfeuer für uns vor. -Oh, super!

He is now already preparing the bonfire for us. -Oh, super!

Caption 19, Meine Freundin Conni Conni schläft im Kindergarten

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Da waren auch Kinder. Sie naschten Süßigkeiten und spielten vergnügt am Kamin.

There were children as well. They nibbled candy and played happily by the fireplace.

Caption 17, Märchen - Sagenhaft: Das kleine Mädchen mit den Schwefelhölzern

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Meinen Ofen habe ich auf einhundertachtzig Grad vorgeheizt.

I have preheated my oven to one hundred eighty degrees [Celsius, about three hundred fifty Fahrenheit].

Caption 32, Apfelkuchen: mit Eva

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The word der Ofen refers to a kitchen oven, but it is also short for der Kohleofen ("the coal oven") or der Holzofen ("the wood stove"). As for the wood that is used for the fire, there are a few different words, including das Feuerholz, das Kaminholz, or das Brennholz. 

Er lief durch die Wüste und sammelte Feuerholz, um es zu verkaufen.

He was walking through the desert collecting firewood in order to sell it.

Caption 6, Märchen - Sagenhaft: Ali Baba und die 40 Räuber

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The verb used for lighting a fire is the same as lighting a match or candle: anzünden. 

Wir haben jedes Jahr im Advent Stollen gegessen und die Kerzen am Adventskranz angezündet.

We ate stollen every year during Advent and lit the candles on the Advent wreath.

Captions 24-25, Nicos Weg: Lieblingsfeste

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Wir benutzen sie, um ein Feuer anzuzünden.

We use them to light a fire.

Caption 29, Deutsch mit Eylin: Denk schnell!

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Two more relevant nouns are der Schornstein ("the chimney") and die Glut, which is a singular word for embers. 

Da entdeckte der Wolf den Schornstein.

Then the Wolf discovered the chimney.

Caption 66, Märchen - Sagenhaft: Die drei kleinen Schweinchen

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Absolute Spitze ist das Team „Gut Glut“.

The team "Gut Glut" ["Good Glows" or "Good Embers“] is absolutely great.

Caption 16, Deutscher Grillmeister: Es geht um die Wurst

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Further Learning
You'll find more examples of all of these words used in context on Yabla German.

The phrase above, often written colloquially as "Thar she blows," comes from the classic 19th century American novel Moby Dick, written by Herman Melville. It refers to an exclamation made by whalers at sea in the 19th century when they spotted a whale to hunt, a practice now fortunately outlawed by most countries in the world. When whales—or dolphins—surface, some species blow air and water condensation into the air in a visible stream.

In German, the verb "to blow" can be translated with a variety of words, depending upon the context. You're probably already familiar with sich die Nase putzen, which means "to blow one's nose," literally "to clean one's nose." Let's take a look today at  some other German verbs that are often translated as "to blow."

Sie hören sogar einen Baum, der vor ihnen steht, weil der Wind, der um den Baum weht, ein Geräusch macht.

They can even hear a tree that is in front of them, because the wind that blows around the tree makes a noise.

Captions 47-48, Meine Freundin Conni: Conni schläft im Kindergarten

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The verb wehen is the usual term for the wind blowing.

Der Wind pustet ordentlich Sauerstoff in unsere verschmutzte Luft.

The wind blows lots of oxygen into our polluted air.

Caption 15, Piggeldy und Frederick: Aufräumen

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Here, the translator chose to translate the verb pusten as "to blow," but it could also have been translated as "to puff," a more common translation for this word.

Und weil in der mit 500 Metern über dem Meeresspiegel höchstgelegenen Stadt Hessens der Wind so kräftig bläst.

And since, at 500 meters above sea level, Hessen's city with the highest elevation, the wind blows so strongly.

Captions 5-6, Energiewende in Hessen: Windräder und Solarparks

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Here, the translator chose to translate the German verb blasen as "to blow," a verb related to the noun die Blase, which means "bubble." In fact, the blowhole of a whale is called das Blasloch, and the act of blowing out air and condensed moisture is called der Blas.

Zu spät, denn mitten in dem letzten Angriff pfeift Mr. Attwell ab und die Deutschen waren bedient.

Too late, because in the middle of the last attack, Mr. Attwell blows the final whistle.

Caption 27, Fußball: U21-Nationalmannschaft

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The verb pfeifen means to whistle, but it also means "to blow a whistle."  If a referee blows a whistle for a foul, you'd say er pfeift ein Foul. The verb abpfeifen above means "to blow a whistle to stop the play," "to signal the halftime," or "to end the game."

Wie schön ist doch die Welt, alles löst sich in Wohlgefallen auf.

How beautiful the world is, everything blows over.

Captions 43-44, Großstadtrevier: Alle für einen

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The idiom sich in Wohlgefallen auflösen literally means "to dissolve in pleasure," but is often translated with the English idiom "to vanish into thin air" or "to go up in smoke." Here, the translator nicely chose to use the idiom "to blow over."

Wenn's nach mir ginge, würde ich ihn lieber heute als morgen in die Luft sprengen.

If it were up to me, I would rather blow him up today than tomorrow.

Captions 62-63, Die Stunde der Offiziere: Dokudrama über den 20. Juli 1944

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The verb sprengen (as well as in die Luft sprengen) means "to blow up" or to explode something. Although murder is an extreme means of regime change, killing the person in the case above could probably be seen as justifiable, given the millions of lives at stake.

Further Learning
Go to Yabla German and search for the verb "to blow" in a variety of conjugations, such "blow," "blows," and "blown." You can also expand your knowledge of how some of the other German verbs above can alternately be translated by looking up, in various conjugations, the verbs putzen, wehen, pusten, blasen, pfeifen, and sprengen.