I am not familiar with e-mail but I need to test Email client for mobile platform. I suppose that there are some test engineers which can help me to define tricky use cases and well-known problems which could occur. And which articles and standards do I need to learn for better understanding?
Your question is rather vague. There are different types of email protocols, and your overall test strategy depends on which protocol(s) your client supports.
But, some basic areas for testing email clients on a mobile device include
Of course this list assumes that you are very familiar with email functionality, and email protocols.
A partial answer: email rendering is very important. Many emails, like newsletters, marketing materials, etc put a lot of effort to make their emails beautiful. Having the HTML render properly on a mobile client takes effort.
One type of test is the acid test: http://www.email-standards.org/acid-test/ You could also do side-by-side comparisons for many marketing emails, from well known email providers like mailchimp, etc...