What is the proper way to ask for ideas for a research topic to a professor on a different institution that I have no connection with? I am planning to start a new project on a certain topic, which nobody in my institution is an expert in. I have spent several weeks on literature research on this topic (by superficially reading papers without studying them), however it is very hard and inefficient to find a well-defined problem all by myself. 

So I need help from an expert, currently my knowledge on this specific topic is very superficial. I plan to properly get my self ready while doing the research after I find a well-defined problem, because without a well-defined problem it is very hard to make a structured well-defined path, I would end up wasting time by jumping from one paper to another blindly (I have been there). 

I have prepared several questions related to this topic that may lead to a research problem, however it is very likely that those questions are very ignorant. 

I have sent emails to several people, after the first email they usually respond but when I send those long questions I don't hear from them anymore.

So I would like to learn what is the proper way to ask a an expert that I haven't met before, for a help direction guidance to find a well-defined problem?

The thing is, I really need this problem on that specific topic, because of several reasons, I tried to find by myself, but without proper experience in that field, it is hard and extremely inefficient. Also, I know it is something pretty unusual but I must find this problem, and I know for an expert it would be pretty straightforward. Any advice would be great!

edit:
I need this specific topic because, I have finished the first year of my 3 year PhD, and so far it was jumping from one project to another randomly with the direction my advisor, and it was mostly a dead end. Thus I need a well-defined project that puts me on a track and helps to have a good understanding of my current field. Currently, what I do is not efficient, I am not learning the important first principles of the field it is just random drafting. I need a systematic, structured path. It is hard to explain without telling the specifics. But that certain topic I want is not that a narrow topic it is quite broad. and if someone spends a year on a project involving that topic, he would really have a very good understanding of the overall field that I am working on. I mean that topic, would really teach most of the very important fundamentals, also would be really beneficial. 

To explain this more, what I am doing now is like watching a tv series starting from episode 150, so it makes some sense but always something is missing, in order to get the overall picture in order to have a bottom-up approach I have to start from episode 1. And that specific topic would provide that. There are a lot of papers coming out on that topic I know there are accessible problems for a PhD student without a deep background on that topic. The matter is, this is getting out of scope but, I know I can have a very good productive PhD. But as things going now it is not going well. I am certain if I keep doing what I am doing at the end I will be one of the failed PhD's. So I think I have to take the wheel and make good plan respect to my aims. And I think a project on that rigorous topic that will teach most of the fundamentals of my field, also which will give a deep insight and the first principles would be really what I need. Otherwise, this PhD and my career, my potential(?) are just fading away. I mean PhD is knowing something very well, but currently for me, it was just having superficial ideas on a lot of different stuff. So I have to turn things around. Focus on this important topic, which will help me to be very good on one thing.
While it would be nice to imagine that we all do research for the betterment of mankind, the reality is that it is often transactional. This is because you’re asking for some stranger’s time and efforts, and they don’t see why they should give it to you. 

If you manage to show them that you are able to come up with non trivial results by yourself, or offer them some indication that they’ll get something out of it (a publication hopefully), you might get a chance. 

The reason that this is the way things are is because professors get approached with these requests all the time, and they have to prioritize them. First dibs go to their own inner circle of collaborators. Guess what circle random strangers are on? 

If professors responded seriously to each such request they’ll end up with no time, and because most of these requests end up as dead ends, they tend to be wary of allocating their efforts to high risk collaborations such as the one you’re offering. 

Good luck!

EDIT: if you really want to impress a professor, take their class and shine! Alternatively, open a literature review, and start doing the hard work of familiarizing yourself with the field. You’ll need to anyway if there’s gonna be a paper coming out of it. Also, write down your thoughts. Start a draft paper and write down your initial ideas. What is the problem? Why is it important? What is your proposed solution? Even if it’s a draft or rough or stupid to you, just write. Then you can send this to professors! This tells them two things: you’re serious about this and that you can formally write out your thoughts. It’ll also help you crystallize what exactly is it that you want to do.