Fall 2018 application cycle has started and I have a couple of (hopefully not too specific) questions regarding recommendation letters. I am applying for a PhD position in pure mathematics in the USA, with lots of top schools included.
(1) Does the status of the letter writer matter greatly to admission committees? For example, I have done research with a full professor, an assistant professor and a lecturer in my department. The latter two got their PhDs in 2011. If the three of them write me a letter, does that automatically put me at a disadvantage because two of them are not full professors or one of them is a lecturer? I have heard that, in principle, letters from people that are known in their field are looked upon more favorably by committees, particularly because they might be familiar with the letter-writer and can 'read between the lines' and get more information out of the letter.
(2) Should I bother asking for a letter from professors that only know me through classes? I have a potential fourth person in mind for a letter - he is a professor I took two classes with and did well in both. In my understanding, "so-and-so was a good student in my X and Y class" will probably impress no-one, even if it comes from an established professor. All programs require 3 recommendation letters, so would you think it is worth the effort to have an extra letter if it comes from such a professor?
Thanks in advance for any responses.