Is WebP smaller than JPG?
For screenshots, graphics and anything with transparency, usually by half or more. For photos it depends on the quality you pick, since the same number does not mean the same quality in both. Convert a few and read the sizes, or set a size limit and let the quality follow.
Will every browser and app show WebP?
Every current browser shows it. Some older editors, upload forms and email programs still refuse it, and for those a JPG is the safer file to send.
Does PNG to WebP keep transparency?
Yes. The see-through areas stay see-through, which JPG cannot do, so a logo or an icon can go to WebP and stay small without a background colour.