Electrical "load" is commonly defined as power dissipated by the powered equipment or device. Increasing the load on the secondary will increase both secondary and primary current.
Primary current divided by secondary current = number of secondary turns in the transformer divided by number of primary turns.
Yes and is directly proportionally with the ratio of voltages, e.g..480 to 240 v sec twice as much current on the secondary 2:1 ratio
Yes, in a special transformer called a magnetic ballast. It is designed to limit the flow of current through a discharge lamp, like a mercury vapor lamp, high pressure sodium lamp etc. Otherwise, the current would increase without limit after the igniter ionized the gas in the lamp