Hi @Robster, Thanks for the info! It sounds like there may be a browser extension interfering with the Webflow Designer. Have you tried disabling any of your extensions? This might be helpful: Troubleshoot website performance issues | Webflow University
As for your questions:
(1) The Designer is supported in Chrome and Safari 7+ and sites built in Webflow work across all major modern browsers. More info here: Intro to the Designer | Webflow University
(2) The only things that do not show in the Webflow Designer are custom code related. To view custom code or embedded code, you have to view the published site. We’re definitely looking to make improvements in this area though. If you have time, add your thoughts to this thread: http://forum.webflow.com/t/live-code-editor/1260
(3) This is 100% achievable using Webflow, but depends on the user’s skill level. 
I hope this helps.