What's the purpose of 来 in the following sentences?
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"来" has multiple meanings and uses. https://www.zdic.net/hans/%E6%9D%A5
买来, 买什么来 - "bought-in", "bought what in". 他给我买什么来了？ What has he bought in for me?
用在另一动词前，表示要做某件事 (Do, or willing/eager to do, something)。
我汉字写得太慢。你来写吧。- My writing is too slow, You do the writing instead.
我来买票. - I do the ticket purchasing. (Let me purchase the ticket).
2 & 3. Used before a verb to express volition.
讓我來做吧。 / 让我来做吧。 ― Ràng wǒ lái zuò ba. ― Let me do it. (Wiktionary)
去 and 来 are both often used in Chinese to indicate the direction of motion.
你过来： you pass from: come here
我过去： I pass to: I'm coming
Older English had hence = 去 = to and hither = 来 = from, also whence and whither, but these are hardly used nowadays.
Hie thee hence = go you from: go away
come hither = come from: come here
German hin means: direction to or towards something: 去
German her (say the same as English hair) means: direction away, from where you are：来
Maybe, in your language, you have similar words to indicate direction.
In translation, these directional forms of 来 and 去 often get lost.
他给我买什么来了？ 买来 = buy from
you for me buy what from le
Was hast du mir gekauft?
What did you buy for me?
多少钱能买来快乐？买来 = buy from
much little money can buy from happiness?
Für wieviel Geld ist Glück zu haben?
How much money buys happiness？
我汉字写得太慢。你来写吧。来写 = come (to) write
I Chinese characters write de very slow. you come write ok
Ich bin sehr langsam in Chinesisch schreiben. Schreib du doch.
I'm pretty slow at writing Chinese. You write it.
我坐下来写信求情。下来 = down from
I sit down from write letter ask favour
Ich saß mich hin um einen Brief zu schreiben, eine Bitte um einen Gefallen.
I sat down to write a letter asking for a favour.
我来买票. 来买 = come (to) buy
I come buy ticket
Ich bin gekommen um eine Fahrkarte/Eintrittskarte zukaufen.
I've come to buy a ticket.
你来干什么？来干 = come (to) do
you come do what
Was willst du?
What do you want?
我来买饮料。来买 = come (to) buy
I come buy drinks
I möchte Getränke kaufen.
I've come to buy some drinks.
In fact, the distinction between come and from is unclear and artificial, because, any time you come, you from, so to speak. You can't come to somewhere without moving from somewhere else.