In this exact wording would invokes the future - the waiter is asking what you want in your coffee (milk,cream,sugar, etc).
It could also be used for emphasis after say you've been discussing the various merits of having coffee in various ways, and you'd put stress on the word.
How would you like you coffee?
But it still has the same meaning.
Neither is right. You do not "request...to...". You "request that...".
Your two examples also have different meanings. The first one indicates that the user will be kind in sending feedback. The second says that you are asking kindly (meaning politely) for feedback.
You can instead say
We kindly request that you send us feedback.
Which is the most natural and formal rewriting. If there is a previously mentioned feedback that we are referring to, we can say
We kindly request that you send the feedback to us.
If you are intent on using "to," then you can use it with "ask."
We kindly ask you to send us feedback
But it's strange to use "kindly" with the less formal "ask."
================ Edit: additional info about kindly ===============
Kindly is a little bit of an archaic word in both the context of kindly asking someone to do something and asking someone to kindly do something.
Kindly asking someone to do something is used frequently in written English, especially formal English. It just means you are asking them politely. Here the archaic nature of the usage lends the word its formality. "We kindly ask that you..." is used in a lot of official or formal correspondence when the speaker is emphasizing that they do not wish to bully you.
Asking someone to kindly do something is less common but could also appear in written, formal language or in sarcastic language. Asking someone to kindly do something is frequently used in old movies and books by a stuffy schoolmarm asking children to kindly pay attention or kindly sit up straight. I would suggest that you avoid it unless you are speaking to people who are not native English speakers and therefore think it is common and polite usage.
The statement by both you and the writer of the page that you reference indicating that you do not need to be kind to ask is based on faulty logic. When you "kindly ask" it means "politely ask," so don't base your choice on the literal meaning of the word in isolation. Does the person have to do what you are requesting kindly? No, they don't. They may respond rudely--it's their choice and if you are polite you will accept either a rude or a kind response. By instructing them to do something kindly you are talking down to them in a way that is not frequently done in modern English.
I notice that the link you sent seems to be written by Indians about Indian English. Because India is a nation that speaks English as a second language, Indian English has a lot of quirks that the rest of the English-speaking world would consider incorrect. If you plan to speak exclusively with people from India/Pakistan, then you may want to use what is accepted there, regardless of whether a native English speaker would say it is correct.
Best Answer
First, let's start with a declarative main clause:
We'll turn it into a question by replacing this with what:
But this sort of question is only allowed under special circumstances – for example, if you couldn't hear what someone said, or if you wanted to express incredulity at what they said.
Let's turn it into a normal question instead (an interrogative clause):
We did two things here:
We had to do step #2 because this was a main clause; main clause interrogatives are marked by subject–auxiliary inversion, unless the wh-phrase is part of the subject.
In your example, we have the same thing, except it's a subordinate clause:
Subordinate interrogatives are not marked by subject–auxiliary inversion, so the only thing we need to do here is move what to the front. The subject and auxiliary remain in their original order: it's, not is it.
Your version is the same thing, but it omits the subject it:
Here, the ∅ symbol indicates that something has been left out. However, there is nothing that would allow you to omit the subject here, so your example is ungrammatical.
In this answer, the * symbol indicates that a sentence is ungrammatical.