die Banane
banana
A long, curved tropical fruit with a yellow peel and soft, starchy flesh.
Zum Frühstück esse ich gerne ein Müsli mit einer geschnittenen Banane.
For breakfast, I like to eat muesli with a sliced banana.

banana
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banana
A long, curved tropical fruit with a yellow peel and soft, starchy flesh.
Zum Frühstück esse ich gerne ein Müsli mit einer geschnittenen Banane.
For breakfast, I like to eat muesli with a sliced banana.

In the meaning of 'egal' (irrelevant / doesn't matter) or 'unsinnig' (nonsensical), 'Banane' (banana) is purely colloquial. It is used in informal conversations with friends or family, but not in formal or written contexts.
Ach, deine Sorgen sind doch Banane, das wird schon alles gut gehen.
Oh, your worries are nonsense; everything will be fine.
In the colloquial meaning, 'Banane' (crazy / nonsense) is used like an adjective after the verb 'sein' (to be). The typical structure is: 'Etwas ist (völlig/total) Banane.' (Something is completely/totally crazy/irrelevant.)
Ob du das heute oder morgen machst, ist doch völlig Banane.
Whether you do it today or tomorrow is completely irrelevant.
When referring to the fruit, typical verbs are 'eine Banane essen' (to eat a banana), 'eine Banane schälen' (to peel a banana), or 'eine Banane schneiden' (to cut/slice a banana).
Ein Affe im Zoo schält gerade eine Banane.
A monkey at the zoo is peeling a banana right now.
indifferent / no matter
'egal' and 'Banane' can both express colloquially that something is not important. But 'egal' is the normal, clear word. 'Banane' sounds very casual and is more often used in fixed expressions like 'Das ist mir Banane' (I don't care / it doesn't matter to me). Learners may confuse the words because the attitude being expressed is similar. The important point is: 'Banane' is actually a noun and sounds slangy in this meaning; in neutral situations, it is better to say 'egal'.

Nach der Arbeit ist mir Banane, welchen Film wir sehen.
After work, I don't care which movie we watch.
Am Wochenende war mir egal, wer den Haushalt zuerst macht.
On the weekend, I didn't care who did the housework first.