Citation to well-known results and reference to user manuals There are some very well-known results and equations, e.g., Shanon Capacity formula, Erlang Distribution and Poisson Distribution, etc. Do we have to provide a reference for these results as well?

Also at times we seek help from a user manual while writing a simulation program or conducting a practical experiment. Do we have to provide reference for user manuals as well?
My first comment will be that it is better to add one reference too many than one too few. Reviewers or editors might suggest to remove references during the review process if they seem superfluous. 

In some cases, it might be more useful to add references to quite basic concepts. One such instance is when papers are directed at least partially to people outside the field. In such cases it may be sufficient to point at a basic book in the field, as an example to point to a good book on statistics regarding the Poisson distribution (the book has to provide some good information on the topic of course). This can help people who may have a different background to get deeper into the topic. 

In general there is of course a fine line where references are or are not needed and with time one learns to identify this line better. What you can do is to simply look at other papers that you have read and see where they place the line and try to follow their example. That will likely form a very good basis for finding the right level of referencing. But, be aware that the line is different depending on the audience of the publication where the paper is published and you should briefly check to see what is applicable in each journal where you publish.