What is this schematic symbol? Transistor ? Variable Inductor
Is this a PNP transistor? looking up the model number doesn't give much 
  


Building up on the comment of Harry Svensson and jonk, this is a mesa PNP transistor. The MESA technique, in the early days of the transistor, was a technique developed for improve the (then poor) HF response of the devices by removing those parts of the base region which, for their geometric structure, do not improve the \$\beta\$ current gain and rise too much the stored base charge \$Q_{bb}\$ and the base-collector capacitance \$C_{bc}\$, raising the switching time and lowering the cut-off frequency of the device, resulting in its general slowing down. The technique consist of etching of the semiconductor around the emitter and the base contacts: this creates a sort of plateau respect to the collector region on the wafer around these contacts, and the Spanish word for this is "mesa".


  
  Is this some kind of variable resistor or variable inductor? 
  


This is precisely an analog delay line: it is a network which, within given frequency range and reasonable waveform distortion, produces at its output(s) a delayed version of its input signal, i.e.
$$
v_o(t)=v_i(t-t_D)
$$
where \$t_D\$ is the characteristic delay of the line. The model shown seems to be a multiple tap delay line i.e. a delay line offering \$n\$ outputs delayed respect to the input by increasing delay times, i.e.
$$
\begin{split}
v_{o1}(t)&amp;=v_i(t-t_D)\\
v_{o2}(t)&amp;=v_i(t-t_{D1})=v_i(t-(t_{D1}+t_{D2}))\\
v_{o3}(t)&amp;=v_i(t-t_{D1})=v_i(t-(t_{D1}+t_{D2}))\\
\vdots\quad &amp; \qquad\qquad\qquad\vdots\\
v_{oN}(t)&amp;=v_i(t-t_{DN})=v_i\left(t-\sum_{i=1}^Nt_{Di}\right)\\
\vdots\quad &amp; \qquad\qquad\qquad\vdots\\
\end{split}
$$
In the case under examination, \$DE1\$ seems a 4-tap delay line where each tap adds a \$50\mathrm{ns}\$ delay respect to the preceding one.