This is Indian English. See Vishy's Indian English Dictionary.
July 12, 2006
Vishy's Indian English
Dictionary: doubt
doubt. /DOWT/. A question asking for
clarification. In standard English and
American, the noun doubt is
uncountable and refers to a lack of
complete trust in something. Doubt may
be expressed as simply as doubting
someone's abilities or as profoundly
as someone doubting their own
religious faith. Not so in India. In
India, doubt can be used as a
countable noun. When a school teacher
goes over an intricate concept in
class, she invariably leaves some
students with doubts in their mind
about their understanding of the
material just covered. Students ask
her questions to get a better
understanding of the concept and each
such question is called a doubt. It is
entirely normal to hear a statement
like "I have just one doubt, miss" or
"If you have any doubts before the
exam tomorrow, come see me in the
staff room". The doubts in the
aforementioned sentences are not as
much rooted in a lack of faith as in a
lack of understanding. Attentive
readers would have encountered the
Indian English sense of doubt a fair
bit on online message boards in
threads started by Indians. Titles
such as "Visual Basic .NET/Oracle
doubt" are not uncommon for threads on
programming-related message boards. It
is my understanding that this sense is
mostly prevalent in southern India,
but I could be wrong on this count.
The meaning of kindly is hopefully clear: "kindly help me" means "please be kind and help me" (or "please help me out of kindness"), etc. It's a word used for polite requests; a bare "help me" is impolite relative to "kindly help me".
If you're asking why kindly is more common in Indian English than elsewhere, it's just one of the hundreds of things that have remained in Indian English long after they have gone out of fashion elsewhere.
Searching Google Books for "kindly do this" and looking through the first ten pages, most results, besides a few from India, seem to be from British and some American books, pre-1920. Examples:
"If our friends will kindly do this for us, we shall feel indebted to them." [The Penny Protestant operative, 1842]
"Would you kindly do this?" [Letter from Florence Nightingale, ≈1886]
"If you will kindly do this, I will be very thankful" [Southern and Southwestern Railway Club, Atlanta, 1914]
"If you will kindly do this I will pay you for the two together" [Anthony Trollope, 1864]
"Would you kindly do this library another favor and again place it under obligation?" [Washington State Traveling Library, 1913]
and so on and on (there are hundreds of results), and most interestingly, one 1886 book showing it must have been standard in England:
The first thing that strikes you on landing in America is the want of deference and courtesy among all classes. Not only from the inferior to the superior, but vice versa also. The maxim noblesse oblige has no sway there. In England, speaking to an equal or a social inferior, "Kindly do this," or "Please give me that," is general. In America the "kindly" and "please" are carefully omitted…
[From context, he doesn't mean it's used only with inferiors, but even with inferiors.]
Anyway, given that kindly was standard, this word for politeness entered India when English did—during colonial rule—and it has stayed on. Why something has continued to exist is not a question that can be answered (inertia?); perhaps the right question is why it went out fashion in the UK and US. (And I'd be interested to learn.) My guess is that either the phrase became clichéd, or such politeness came to be deemed excessive. In the US it seems to have taken on a slightly sarcastic meaning: Wiktionary says
kindly
2. (US) Please; used to make a polite request.
Kindly refrain from walking on the grass.
Kindly move your car out of the front yard.
Usage notes
(please): Kindly is used in a slightly more peremptory way than please. It is generally used to introduce a request with which the person addressed is expected to comply, and takes the edge off what would otherwise be a command.
Well, in Indian English it happens to have retained its original meaning, is not peremptory, and is a request rather than an expectation. (And in general it seems safe to assume that Indian English expressions are not sarcastic, and to take them at face value.)
Best Answer
Indian English is sometimes hard to digest for native speakers. But it is not as difficult as it seems.
From this old ELU question and Vishy's Indian English Dictionary
My Views
The author of Vishy's Indian English Dictionary claims that this sort of usage is mostly prevalent in southern India, which is actually quite true. I am from the southern part of India and in Tamil, the direct translation of doubt is Cantēkam. In schools, colleges and even offices (in TamilNadu), when someone gives a set of instructions or lectures a large group, at the end, 99 out of 100 times, they will ask
which directly translates in English to
Note: Apologies for quoting a phrase from another language. But I am trying to explain how I think it all started.
With the advent of Internet(that transcended race, color, sex, religion and all those), more Indians began interacting with native speakers. And when they had questions in their mind, their brain fired the familiar "ask-him-the-doubt" neuron and eventually they ended up saying - "Hey Mark! I have a few doubts". And since Mark, who would have gotten offended because some Indian person had a few "doubts" despite such a lucid presentation of his thoughts, his reaction would have been "Excuse me? You have doubts?". Looking at a baffled and bemused Mark, our Indian friend too would have been perplexed, unaware that "doubts" implies "uncertainties" to native speakers and responded with "Chill man! Just a few questions.." (think damage-control).
It's more of a Mother Tongue Influence and cultural effect. I say this because, as non-native speakers, we tend to think of words in our native language (say Hindi or Tamil), and then translate it to English(word-for-word), applying the synatxes and semantics, ensuring that intended recipients and listeners get the message. But sometimes, it so happens that, a legitimate phrase in InE(such as this, "to have doubts") becomes confusing to speakers of AmE/BrE.
Disclaimer : Mark and the Indian guy are used as examples for narrative purposes only. Any resemblance to living person is purely co-incidental.
To answer the OP's Questions
Although the scenario seems illogical(personally), this is right, purely because doubts directly translates to questions in InE.
Why I feel this particular scenario is a bit flawed, even for InE
Purely because, I think you capture a spy and grill the daylights out of him. So you question him hard, shooting questions left, right and center, perpetually threatening to end his life if he doesn't comply. Let me tell you one more thing - Mostly, (read MOSTLY), the conservative Indian culture(of course, now people are opening up, thanks to the Internet and globalization) prevents most of us from asking our doubts(questions) freely. We hesitate a lot. Sometimes and in some parts of India, asking questions to an elder or a professor or a lecturer is even frowned upon. But in this scenario, you don't hesitate to ask your doubts(questions) to the captive. That's why I said this scenario looks wrong even though the sentence would be valid in InE.
@Mr. Shiny and New... Certain or uncertain, wholly known or partially known is irrelevant. Doubts(questions) can arise in your mind any time about anything. You may be a beginner or you may be a Subject Matter Expert. Doesn't matter. You ask your doubts to the concerned authority whomsoever it may be, trusting that they will have the answers to clarify your queries. Period.
No. You captured and questioned a spy for hours. The verb form of doubt is incorrect in InE.
However,
is correct.
Conclusion:
In InE, Doubts are used as nouns. They are nothing but "questions", which needs answers or clarifications to be made.
Update1: I have edited my answers to be on-topic. I did not intend to digress.
Here's a list of Indianisms that you will find funny, absurd, totally wrong, may be even provocative to an extent but these totally get the message across to the intended parties in InE.
Update2 : Added new points and perspectives to the answer. Not sure if it appeals to readers but nonetheless I am sharing my experience as an Indian English speaker.
Update3 : Added clarification and details as to why I think OP's second example seems illogical to me.