Haxe is just a language. However, there are several graphical frameworks that allow for that. Dicey Dungeons (his newest game) is specifically built off the OpenFL framework which tries to replicate the Flash API.
I always used the Flash WYSISWYG editor for the canvas and graphics, so OpenFL isn't a replacement at all in that respect.
Same here. I remember implememting the game loop using one or two timeline frames.
You can actually create graphics in the Flash WYSIWYG editor and import them into OpenFL. You won't get the exact same workflow, but it's not completely lacking the visual tooling either.
OpenFL, a library for Haxe that implements the Flash API, includes a mechanism to import graphics drawn with Flash's original tooling.