REW issues - popping, static in frequency sweep output.

OP:

I don’t understand. How else would I get a sweep test tone from REW installed on my PC to play through my speakers but via my integrated amp? 

That answers my question.  No, you did not connect your speakers directly to your laptop.  You have an amplifier in the middle, which is correct. 

btw the popping noises have nothing to do with connecting to my integrated. The popping is present on my laptop speakers/ear buds when USB mic is connected and goes away when I unplug the mic.

This sounds like a potential internal power issue.  Really suggest you go the external DAC route. 

Another low cost option to try, is if you have a powered USB hub.  It doesn't rely on your laptop's USB 5V supply.  

I installed ASIO drivers and while REW sees them, it doesn't produce any sound. The REW developer responded and has requested screen s shots of the sound card preferences - stay tuned. 

Been a while since I have done this. Did you configure the asio settings? See link.

Configure

From REW support:

The base Java drivers only deliver 16-bit data, the EXCL device entries deliver the full capability of the device. Neither require changing the device bit depth.

You can't use a native ASIO driver because ASIO requires input and output to be on the same device. Your Java settings look fine.

Popping is typically caused by another process taking up so much CPU time that REW is shut out long enough for data to be lost. That wouldn't be affected by whether or not the mic was connected though. Latencymon can show you whether that's an issue.