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I don't understand the usage of auxiliary verbs in questions that begin with How ("How ...?"), and always use structures such as:
How to learn play piano?
How long it take to deliver product?
Do these questions require do/does or may/can?
Where do we place them in our sentences, if they're necessary?
Questions starting with "how", specifically, the ones you use as examples, require an auxiliary verb. It should be placed immediately after "how", followed by the subject, then the verb. Which auxiliary verb you need depends on two factors, namely:
Assuming you want to ask your first example in present tense, you should say
How long does it take to learn to play the piano?
Maybe you can write your second example in the correct way as a comment to this answer.
After another round of search, I found similar questions:
As JMB says in his answer, "how" questions require an "auxiliary verb" in front of the "subject" (the structure which I previously misunderstood):
How do I ask ...?
How should I rewrite ...?
How can I negotiate ...?
To avoid using the pronoun I in these questions, it is possible to rephrase the questions like this:
What is the way to ...?
or like this (asking you instead I):
How would you make ...?
How do you make ...?
