How to export to WebP format from Photoshop preserving color fidelity and optimal quality

I would like to make a few questions for this community regarding WebP for web images:

1. Do you recommend switching over to WebP (from PNG and JPEG) for web images?
   Does it really decrease size preserving quality?
   
   
2. I've realized that when I export to Webp, the colors are a bit off from my Photoshop design, whereas JPEGs seem more color-faithful. What color profile settings (or other settings) could improve the color fidelity of my WebP exports?
   
   
3. I've found that I need to use an external image compressor (such as [removed by moderator]) to get my file to the optimal balance in quality vs size for websites. Is that really necessary, or can I get to an optimal compression using Photoshop WebP export settings alone? What method do you recommend going from Photoshop to an WebP final image optimized for the web?