Does Resolve support a while-recording audio monitor output?

On my Windows 10 Dell Laptop I’ve been able to plug in both an external mike and my headphones via the single 3.5mm audio jack using a purpose-specific (i.e. input and output wired) ”Y” adapter. So, of course, I can record with the mike and LATER hear how it’s going to sound by playing back to the earphones. However, in other recording software I’ve been able to hear the output of the PROCESSED audio as (while) it’s being recorded so you can hear how it’s going to sound (with the equalization, compression, etc. being included in that audio monitoring signal) while speaking into the mike. Is there a way to do a monitoring function like that in Resolve 17 (either in Editor or Fairlight)?

BTW, I was able to hear what I was saying by turning up the Bus1 but:
1. There seemed to be a slight delay between a tap on the microphone and the sound on my earphones (and the earphones are not bluetooth so they don't add the delay).
2. In this setup (described above) when I tap on the microphone the meter goes to a peak, falls and then goes up almost as far again. When you say a 1 syllable word like "test" you get the word repeated like an echo (reverb is disabled).

(I will have the studio version as soon as B&H can ship a card…been waiting a week but, if the answer to this question is different for studio than the free version I have now, keep in mind that a studio solution will help me even if the free version won’t.)
THANK YOU FOR ANY INPUT regarding these 2 issues (monitor signal and unwanted echo)!

As for the first thing you mention this is a known issue called latency and it's not specific to resolve. The roundtrip from the audio input through software processing and back to the audio output always takes some time.

I'm not on Windows but from what I hear Resolve doesn't work with ASIO audio drivers, which will generally introduce less latency than others. If that's the case then you are better off recording in another tool if you want to have software monitoring enabled (=hearing the processed audio, not the input signal).

Try the Auto monitoring option, it may help.