Yes this metal is formed around the steel core (which is magnetic) and then thinly coated with zinc (providing the steel protection against corrossion).
Yes galvanized steel is magnetic. Almost all kinds of metal have a magnetic pull. Be carefull using galvanized steel though, when heated it can be very toxic. Don't try to weild with it. Very dangerous.
It is super-important not to heat or weld galvanized metal. I did this when I was about 16 years old and that night, I was running a fever of 106 degrees, and deathly ill.