kosten
to cost
To have a particular price in money.
Was kostet dieses Buch?
What does this book cost?

to cost / taste
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to cost
To have a particular price in money.
Was kostet dieses Buch?
What does this book cost?

In the meanings 'einen Preis haben' (to have a price) (m01) and 'Aufwand erfordern' (to require effort) (m03), 'kosten' (to cost) requires two accusative objects: the person (whom?) and the thing (what?). For example: Es kostet mich (accusative) viel Zeit (accusative).
Die Reparatur hat mich fast 100 Euro gekostet.
The repair cost me almost 100 euros.
The meaning 'probieren' (to taste/try) (m02) always refers to food or drink. The other meanings (m01, m03) refer to price or effort and often have a person as an additional accusative object.
Darf ich mal von deinem Eis kosten?
May I taste some of your ice cream?
When trying something to check the flavor, 'kosten' (to taste) is often used with the preposition 'von' (of/from) and the dative. However, it can also be used directly with an accusative object.
Der Koch kostete von der Soße und fügte noch etwas Salz hinzu.
The cook tasted the sauce and added a little more salt.
to need
'brauchen' and 'kosten' can both express that time, money, or energy is necessary for something. 'brauchen' emphasizes more that something is needed, or that you use a certain amount of time or a certain quantity for a task. 'kosten' is especially appropriate for a price in money, or for effort, trouble, or loss. The words can be confused because, for example, you can say both 'Das braucht Zeit' (That takes time) and 'Das kostet Zeit' (That costs time). 'brauchen' sounds more neutral here, while 'kosten' emphasizes more strongly that something involves effort or has a price.

Das neue Ticket kostet am Montag fünf Euro mehr.
The new ticket costs five euros more on Monday.
Für die Reparatur brauche ich noch zwei Stunden.
I still need two more hours for the repair.