Looks like Edge only prefetches when specific link tags give prefetch prompts (Resource Actions per W3C specs) whilst Chrome appears to do things more speculatively.
I don't know about that, there may be extensions or add ons that provide such features though.
Many browsers will start loading a URL as soon as you type it in, even if you don't press enter however, try this with a local server sometime, it can be a little jarring.