Correct abbrevation of academic titles, e.g., “B.Sc.” vs “BS”
It depends on the degree and the context.  Different institutions sometimes have different conventions for abbreviating their degree names.  For example, Harvard writes A.B. while Yale writes B.A.  It's conventional to use the abbreviation suggested by the university that awarded the degree.

Issues such as the use of periods are a matter of style.  If you are writing for publication, you should follow the publisher's house style.  Otherwise, you can decide whether you prefer to use periods.  However, you should keep in mind what other people are doing (for example, including periods is more common in the U.S. than other English-speaking countries).