It is a contraction, but only in speech. You will probably hear someone say "Eu preciso dum segundo," but you will never see it written.
how can i tell the difference between "a" and "one"? I wrote: "I need one second" which was incorrect.
Could this be referring to both time or number? For example could you be asking someone to wait, but also, depending on the context, be asking for a second helping of dinner?
No. This always means that one needs more time and that the other person needs to wait a bit. For another helping, you would probably ask if you could serve yourself again, a question to which any Portuguese person would reply something along the lines of, "Of course! Eat! Eat!" XD
Does anybody else hear SEgundo instead of seGUNdo? Should it not be the latter, according to the rules when there are no acutes or circumflexes?