Remove first occurrence of element from list
That looks mostly right to me. I'll suggest two things.

First, there is nice syntatic sugar for defining functions:

(define (remove-elem xs elem) 
    (cond ...)
)


Save yourself the lambda. 

Second, you are using eq?. That is the wrong checker for this problem. That function returns true if the two objects are the exact same object in memory. It could be true for primitives like ints, but it's not necessarily true. What you want to use is eqv? which will guaranteed work for numbers.