Do fighter jets have forward-looking radar warnings for missiles, and when was this first implemented?
Radar Warning Receiver systems (RWRs) used by military aircraft are omnidirectional. However, they do not warn of incoming missiles (unless that missile is at least semi-actively radar-guided, like an AMRAAM). What they warn of are various patterns of radar activity, including a radar lock (which is a constant, high-intensity scanning of the aircraft's position, more than just a "blip" as the antenna passes by on a wide-angle scan pattern).

If another aircraft has a radar lock on you, you should be expecting an incoming missile of some kind. However, IR missiles (AIM-9 Sidewinder, AA-11 Archer, MICA IR, ASRAAM) do not emit any EMR that indicates they're incoming; they use a passive FLIR sensor to identify and track the heat source they were told to kill (they don't even require a radar lock; the seeker can be cued to a pilot's helmet, or it can be "uncaged" and will lock on to the most significant heat source in front of it). Passive radar-guided missiles like the old AIM-7 Sparrow also do not emit their own radar; they track the radar returns from the firing aircraft. Only semi-active and active radar-homing missiles emit their own radar noise that can be used by the RWR to know one is on the way. A few older passive missile systems used radio control to guide the missile to the target, and RWRs can also detect these "sideband" radio signals as a clue a missile has been launched.

More modern Missile Approach Warning Systems (MAWS) have additional features that can help detect and track incoming missiles of multiple types. The biggest clue of a missile launch is a new heat signature, especially in the direction of an incoming radar lock; a suite of IR sensors can be used by MAWS to put 2 and 2 together and warn you of the missile launch.