From several threads on this forum, it appears that there are two different definations of "flight level". In the USA, flight levels are shortcut phrases for altitudes but only at and above 18,000 feet (Positive Control Airspace). Thus, 18,000 feet is flight level one eight zero. 32,000 feet is flight level three two zero. Below 18,000 feet, altitude is expressed in feet. 12,500 feet would be express as one two thousand, five hundred feet. Apparently, in some other countries, flight levels are used for altitudes below 18,000 feet.
An earlier answer about ILS being "built into runways" is not correct. ILS is a radio beacon system. The transmitter portion of the system, as another poster stated, transmits both horizontal and vertical beams. The ILS transmitter is installed above ground either adjacent to or on the extended centerline for the runway.
The receiver portion of the system is installed in each aircraft. It receives the ILS signal and, depending on the type of instrument being used, either provides a horizontal and vertical needle or other indicia on the instrument that provides information describing the aircraft's position relative to the ideal position, horizontally and vertically, for the landing. The receiver can be slaved to an autopilot and it is up to the autopilot or the actual pilot to interpret the indicia and position the aircraft so a successful approach and landing is made.
In the old days, before flight directors and other sophisticated instrument came into use, this became the source for the aviation term "center the needles". When your ILS needles are centered on the instrument, you are precisely on the course and glide path you need to be for that portion of the approach.
I am not sure I understand the last question. I have never heard the term "watching vectors". A vector, in this context, is an instruction by ATC to turn from current heading to a desired heading, usually with the goal of positioning an aircraft to initiate an approach. Vectors are often also used by ATC to turn aircraft to avoid traffic conflicts. Thus, the ATC instruction: "Wifebeater 201, turn left heading one eight zero, intercept the Wican runway 27 ILS, cleared for the approach" is a vector to immediately turn to 180 degrees and fly that direction until the ILS is intercepted at which time you can fly the published approach for runway 27 at Wican Airport.