Under normal circumstances, though, in order for audio from a capture card to be heard, you do need to have Monitor and Output be on. I'm not sure what you did earlier to hear it without that option, but that is the usual scenario.
If you set all devices to monitor and output, including the capture card, do you hear nothing, or do you hear everything but the capture card?
Beyond that, some notes:
18:20:18.659: ================================
18:20:18.659: Warning: OBS is already running!
18:20:18.659: ================================
18:20:18.659: User is now running multiple instances of OBS!
That is probably to be avoided. Were you intending to run two instances of OBS for some reason?
8:20:18.661: Windows Version: 10.0 Build 17134 (revision: 407; 64-bit)
18:20:18.662: Running as administrator: false
18:20:18.662: Aero is Enabled (Aero is always on for windows 8 and above)
18:20:18.662: Windows 10 Gaming Features:
18:20:18.662: Game DVR: On
Windows is out of date. This means that in addition to the Game DVR feature being on, which negatively impacts performance, Game Mode is also on by default and cannot be turned off. You should run the October 2018 update and turn Game Mode off. This primarily affects capturing local games, but there's no situation in which having it on helps OBS, I don't think.
Both logs contain this line:
18:20:21.945: using video device audio: no
Which means the Elgato is being configured without capturing its audio component. I don't have an Elgato, but on other capture devices there is a configuration option to either activate audio, or to select the proper device from a drop-down list for audio. Check and make sure you've done that, because the above log line seems to indicate it isn't.
The first log says:
18:20:21.945: using video device audio: no
18:20:21.945: audio device: Headset Microphone (HyperX Virtual Surround Sound)
18:20:21.945: sample rate: 44100
The second says:
19:21:26.595: using video device audio: no
19:21:26.595: separate audio filter
19:21:26.595: sample rate: 48000
So it looks like the first time you configured the Elgato, it was set to use a 44.1 hz sample rate and to use your microphone as the audio source?
And the second time, no audio device is specified, but the sample rate is now 48hz.
