Can you tell why the fan load is placed on the emitter instead of the collector ?
It is much easier to make the transistor operate in a linear mode when the load is on the emitter.
(edited for typo)
When is it convenient to configure the load in series to emitter or to collector ?
When the load is connected to the emitter, the voltage gain is 1, so any change in input voltage will result in the same change of output voltage. When the load is connected to the collector, as small change in input voltage will result in a large change in output voltage, but it's not possible to know exactly what input voltage is needed for a particular output voltage, so it is very difficult to make the transistor do anything other than turn fully off or fully on.
How does the base current changes in one or the other layout ?
The gain of a transistor will vary with temperature, and between otherwise identical transistors.
When the load is connected to the emitter, the base current is equal to the load current divided by the transistor gain, so the exact base current will vary, so a circuit needs to allow for a variable base current.
When the load is connected to the collector, the circuit design controls the base current. If too little current is used, the voltage to the load will be reduced, but it's not possible to predict the current needed exactly, so usually the base current is calculated with a safety factor.
What is the emitter voltage when off and when conducting ?
When off, the base and emitter voltages will be zero.
When the TTP223 output is on, the base voltage is set by the potentiometer, and can be anywhere in the range 0 - 5 V. The emitter voltage will be about 0.6 V lower than the base voltage.