[1] In short, I just need to know whether an external DAC (e.g. Fiio E10K) can improve the output of my Edifier 1600T3 speakers (through the normal green wires), my bluetooth TicPods, and my P30 Pro internal speakers. If yes, do I have to purchase extra accessories to connect them?
[2] For external DACs which have mic input, does it mean I get a better signal when recording podcasts with my Zoom H1 and Rode VideoMicro? If not, what is the use case?
Lastly, do these products need to be externally powered or charged?
1. In general: No, it can't. Even very cheap DACs these days have noise and distortion figures way below what any speaker can deliver, even top class studio monitors. However, the amplifier section of the unit can make an audible difference, depending on impedance for example.
2. What will define the quality of a recorded signal is the mic, it's placement relative to the sound source and the mic pre-amp, not a DAC. Therefore, your Zoom and Rode mic are likely to be somewhat better.
[1] DAC is responsible for converting the 0 and 1s in the analog sound wave
[2] Dedicated DAC would usually feature a good dac chip and
[2a] what is important a good power supply.
[2b] Apart from DAC board design good and clean power makes the difference.
[2c] The cleaner the power input, the cleaner the output is.
[3] Unlike digital part where all the 0 and 1s are always the same. The DAC process includes interpolation between the frequency measurment points.
[3a] And the restored wave between the points differs from one chip to another. Leading to different sound signature
[3b] So psu,dac chip and nice board make a combination for a good dac
[4] Having extra stuff DAC amd ADC in the same chassis, sharing the same PSU is similar to using AV receiver as headphone amp. Rather than pure headphone amp
[5] To hear the difference all the components in the system should be good.
[6] And of course wires
they can correct the sound signature but not compleltely change it.
1. Correct.
2. There are only a handful of DAC chip manufacturers and these days, ALL of them are significantly better than "good" (perform significantly beyond audibility). Therefore, any modern DAC will feature a "good dac chip".
2a. Assuming a competent design, then any standard power supply is good.
2b. Any competent board design and psu converts and conditions the power supply, even relatively cheap ones. Therefore:
2c. No, a cleaner power supply makes no audible difference (provided of course it's actually within specification +/- 10% or so), unless you have a DAC that is incompetently designed.
3. There are no "frequency measurement points", the 0's and 1's represent amplitude measurement points.
3a. The original digital audio theorem provided the perfect mathematical solution. In practice, it can't be implemented perfectly but it's extremely close, certainly well beyond audibility and all DAC chips achieved this many years ago. The only exception is DAC chips that provide options in addition to this audibly perfect solution, IE. Different filters deliberately design to colour the sound (reduce fidelity). Therefore,
3b. By definition they cannot have a different sound signature (with the exception of an audiophile DAC deliberately designed to have a lower fidelity).
3c. Agreed. However, as even relatively cheap DACs have competently designed psu's, boards and DAC chips, it's not easy to find a DAC these days that isn't good (from a fidelity perspective).
4. Clearly that's false. If there were a fidelity improvement with separate chassis for ADCs and DACs, then the most exacting/demanding digital audio environments, world class recording studios would use them but they don't, they exclusively use ADCs/DACs in the same chassis!
5. There are no speakers/HPs that good and even if there were, it still wouldn't make an audible difference because the difference is inaudible (to human hearing).
6. Obviously they can't. Wires do not have a brain, artificial intelligence or some sort of magic to analyse what's incorrect about a sound signature and then correct it.
Unfortunately, many of the facts you asserted are false.
G