If your voltage is critical I would go for a higher voltage source and a voltage regulator setup. If you add a big capacitor after the regulator it should take care of the voltage dips that you see.
That depends on what you are doing but 22mA in the worst case is not much at all (thats what a standard LED draws). I don’t know how much the receiver needs but if it is as you say, that the sender needs the most current, then I guess you only need a small capacitor actually, something like 100µF. If you want to you can of course use a 470µF but that would be a little overkill in my opinion.
I can’t answer the question about the Zener Diode/ Resistor regulator because I never used a construction like that.
A voltage regulator I can highly recommend is the LM317. Have a look at the datasheet.
Connect the LM317 as shown in the datasheet (on the very first page). Then your value for R2 would be (assuming you use a 240Ohm resistor for R1):
R2 = (4.5/1.25 -1) * 240 = 624 Ohms
I don’t think you will get a 624 Ohm resistor but you can combine two resistors or use a value thats close to 624Ohms.
EDIT: Maybe a linear voltage regulator like the LM317 is not considerable because the input voltage must be 2V higher than the output voltage. So you must supply the regulator with at least 6.5V, but as Geir has already said a voltage regulator gives you a constant voltage over the whole battery charge (as long as this doesn’t drop below 2V above your output voltage).
Zener diodes…good for VRef, not so much for VReg…I would avoid this option as it’s not suitable for long term use or good design and stability. Get an LDO or use 1.2v NiMh cells and a couple of 4001 diodes.
The decoupling cap on the input side and the output cap make sure that the voltage regulator operates correctly. So yes, you need to add caps to basically every voltage regulator.
The decoupling cap gets rid of the noise and the output cap keeps the voltage stable, as long as it takes the regulator to stabilize the voltage again, if all of a sudden more or less current is drawn.
I’m still learning about electronics too, but as far as I can tell when trying new things at first it probably is going to fail. Then checking the circuit I notice that e.g. I didn’t pay attention to the diodes polarity^^
I don’t know these devices but you should have a look at the formulas in the datasheet of the specific chip, because this calculation is the one used for the LM317.
The internal voltage reference of these devices may be different etc…