I think we'd have to know more about both your environment and the MySQL server's to answer the "Why?". POSIX::strftime honors locale, so the value of $date depends on your LC_foo environment variables. MySQL may be compiled to store utf-8 or some other character encoding.

Question a): I think you should store datetime fields the way MySQL wants, as a datetime column type. Storing them as strings denies you the very useful builtin date & time functions of MySQL. You can retrieve datetimes with MySQL's DATE_FORMAT() function to get most any representation you want. If you have serious encoding problems, you can fall back on unix epoch time for retrieval and then apply localtime.

Question b): Some browsers pretty much ignore http headers. Try specifying the character encoding in the html tag, as well.