This is an extract from a quite technical document. In addition to the problem of understanding the English constructs, you have second challenge in that certain terms have specialised technical meanings. Here we see process being used in a very particular way, as well as processing being used in a subtly different but related way.
In understanding this passage you need to identify the technical terms and establish their meaning in this particular document. You cannot do this simply by reading this one paragraph. We would hope that there would be a glossary for this particular document that would define the terms, however there may well not be one, so instead we at least need to look at a technical dictionary (for example), we cannot simply appeal to standard English usage.
So here you need to know what process, web server, request, concurrent and processing mean.
From my own knowledge of this field the Web Server is a particular process running on a computer, there will be many such processes running. The Web Server has responsibility to receive requests (typically from a Browser) and performs processing to satisfy those requests.
Here we come to the meaning of on behalf which can mean in the interest or aid of. So for each request some processing is done, that processing is on behalf of a single request.
The key idea is that the Web Server is satisfying multiple requests at the same time concurrently. And the issue being addressed is what happens is one request's processing effectively monopolises the Web Server for a period of time, in this case the other requests, concurrently being processed are stalled until the monopolising processing is finished.
Hence to understand this paragraph we need to get definitions of some technical terms but also need some quite detailed technical background information about multi-threaded concurrent processing.
The only slightly tricky English here is the on behalf, which becomes clear when we understand the relationship between a request and its processing.
You are correct in that your example sentence 'The problem with your grade is, you are the person who can fix it.' is not proper English; it should be instead something like 'The problem with your grade is that you are the (only) person who can fix it.'
There are many sentences in English like this where popular or common usage (usually spoken) English will vary from the 'proper rules' of English; this is one of them. The phrase "The problem [with XX] is, ...' is commonly used and quite often omits an implied 'that' following the 'is'.
Best Answer
"We can use while to talk about two longer events or activities happening at the same time" (Cambridge Dictionary).
You can use "while" only in the examples 6, and maybe 4, because only there you have two longer events happening at the same time. (I personally do not feel that crossing the road is a "long event," though). So, both events need to be longer, which means, they are happening in a period of time rather than in a moment of time. But you could also use "when," as in the example 5.
You can always use "when," but you can use "while" only for two longer events.
So, 1, 3, 4, 5 and 6 are correct, but 2 is not.
There's a very clear presentation of using when and while on Grammar-Quizzes.com.