It is a thyristor.
That is the same as an SCR.
Similar to thermistor but has a slightly different operation
No it is not remotely similar to a thermistor. And you do not draw it like that. The gate line is a diagonal line leading to the under side of the cathode.
the buzzer will sound for a predetermined time varying on the capacitor value and the LED will stay lit
You need two circuits, one that will commutate (turn off) the SCR after a pre determined interval. You can do this by having the SCR charge up a capacitor feeding into a unijunction that is wired across the SCR. When it fires the SCR is shorted out and so stops conducting. The other circuit is what you have already. The two are triggered from the same point.