Can you please tell me, what would be the right sentence formation and decent way to ask the following question:
"Have you read the job description properly / thoroughly and got an idea of what I am looking for exactly?"
I would split this question into two questions.
Have you read the job description thoroughly?
Do you understand what I am looking for?
Most job descriptions either do not provide enough detail, or provide too much detail without prioritizing which details are most important. Thus, it is very difficult for someone reading a job description to know what the employer is "looking for exactly". I therefore left out the word "exactly".
This answer changes the questions in five ways:
All of these changes make the questions more formal.
To complete what has already been said, you could use "I wonder whether...", or anything that says that you are thinking this, but you would be willing to accept that it is an incorrect thought (in other words, you are trying not to be accusative, perhaps there is indeed another reason).
I wonder whether [if] you carefully/thoroughly read the job description and got a precise idea of what we are looking for?
Also, it is a good idea to be precise in your question, carefully avoiding words with a connotation of "good and bad". For my part, I like "get a [precise] idea", since it is an clear action, while questioning "understanding" might somehow come across that the person is not intelligent enough.
By contrast, shifting "I" to "we" in the second part of the sentence might be useful to shift the attention away from you (not to make it appear that you are teaching a lesson).
This is, needless to say, a process of trial and error (in which several solutions are possible), and it is never going to come across perfectly (since the person did put themselves in an embarassing situation). But at least, it will come across that you are being considerate.