Is the following question grammatically correct? How + to + verb?
What to buy, where to buy it and (most importantly) how to keep it alive until New Year. Cambridge News
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This is the making of a noun clause using wh- question words (including how).
As you can see, you can make the noun clause by using the infinitive of the verb from the question, then adding the question word from the question.
For example, the verb in the question "do I buy" reverts to its infinitive, "to buy."
Then you tack on the original question word, "What" and you get, "What to buy" from "What + to buy."
The other detail of note in your example is that it is not a complete sentence.
It requires another clause such as, "(We will show you) what to buy, where to buy and how to keep it alive."
In this way, it might be more obvious to see that these had not been questions.
For further reading, you may see, "Forming Noun Clauses from Questions," by Linguistics Girl.