What are those things that look like concatenated hourglasses in the included (TTL) circuit?

f//k knows - and it aint TTL technology

Because they do represent digital switches you notice that they are always used in pairs.
The pair either is a NOT gate if the not switch is on the supply side,
or a YES gate if the not switch is on the earth side.

The reason for grouping them into four blocks is that the circuit design must preclude ANY possibility of a conductive path all the way to earth.

The symbols are transmission gates - just think of them as relays or even transistors.

TTL has nothing to do with this. TTL is based on NAND gates implemented using a weird BJT (transistor) with two bases.

The circuit is in fact typical of CMOS logic and in this context you can reasonably think of a single CMOS FET as a transmission gate (or a relay or a transistor).

I would say those are transmission gates. When the control input is a logic "0", the gate is off (high resistance). When the control is "1", the gate is on (low resistance). If the input goes into a tiny circle, then it is negated.

They are switches, and there are two types. The ones with XX, let the vertical signal pass when the horizontal input is a 1. The other switches with a bubble oXX let the vertical signal pass through when the horizontal input is low (0)