Choosing the right image format can cut your file size in half with no visible quality loss. Here is the simple rule of thumb for photos, graphics and the web.
For the web, usually yes — WebP is typically 25-35% smaller at equal quality and supports transparency. Every modern browser supports it.
No. JPG already discarded some data; converting to PNG only makes the file bigger without restoring quality.
For photos: WebP < JPG < PNG. For logos/flat graphics with few colours: PNG or WebP.