Once the user starts adding the elements, the code becomes easily unstructured, if the editor can have a feature or a plugin that would format the code live while adding the elements this will create a huge difference from a UX perspective

Export / Import files to following systems:

• mega.co.nz https://github.com/tonistiigi/mega
• dropbox
• gist

Add laravel presets
Custom user presets
Custom themes

Case tested on 
Chrome 32.0.7
Firefox 24.3.0
When page is loaded not all elements are loaded, based on the screen resolution,
if i zoom out the browser and reload the page all elements are loaded,
i suggest that you add a fixed side bar that contains an iframe with the elements, could work perfectly

Tabs for JS Code and CSS Code?

I'd recommend splitting the screen in half, top for code bottom with live preview, if idea is considered, i'd recommend not splitting horizontally because users will not be able to preview the col-lg by bootstrap

The will definitely be my most used bootstrap framework, keep it up you are doing a great job.

on the same cdn which you are using for bootstrap you can find a tab which is called bootswatch:
http://www.bootstrapcdn.com/#bootswatch_tab
integration part is extremely easy, replace the link of bootstrap.css with any of the provided bootswatch themes, i think it can be cool for building the structure design then choosing a theme or better inspiration or or or...