That question doesn't really make sense - C2 isn't "with" any particular browser engine, it's designed to work with any standards compliant browser, which includes Gecko (Firefox), Trident (IE), WebKit (Safari) and the soon-to-be Blink (Chrome).
Sharing a .capx is the clearest way to show what you mean and what isn't working.
Note on platforms which support WebGL - which should include CocoonJS in the near future - we manage memory more intelligently by loading all images on a layout-by-layout basis (so images are only loaded/unloaded between layouts). You might find things work better with that.
Yeah. Someone suggested I add an expression to wrap the browser fromCharCode function, but it turns out the browser's function is nearly completely useless. So I'll have to rewrite it to not use that function :P
What exactly have you done and what exactly is wrong? Bear in mind the version from Steam and the version from our site are incompatible. If you bought from our site it won't work on Steam and if you bought from Steam the version from our site won't work.
Why not just type in an X and Y position in the properties bar after pasting?
I'm not sure this makes sense, since the underlying engine is identical on all platforms. The only differences are relatively small, such as a certain object may not work, or the ability to use platform-specific plugins like the Windows 8 object. This is all documented (but lots of people still ask questions about things that are documented :P)
Have a read of Optimisation: don't waste your time. Worrying about this issue is a complete waste of time and will probably never make any difference at all, so use whichever you find most convenient.
Your events don't make sense, unless you have an image point named "loopindex".
This sounds like good news. It sounds like it won't affect Construct 2 directly, but will allow Google to ensure their browser can keep improving quicker than before.
The only thing you can really do to optimise memory use is to use fewer images and fewer animation frames. 68 MB is absolutely massive for a compressed app - decompressed it could be hundreds of megabytes, and mobile devices have very limited memory, so you're trusting Safari to shunt images to and from memory at random times to prevent itself running out of memory.
It's fine to use a layout-sized tiled background. Method 2 of designing your level will probably cause you to go mad, so I'd recommend method 1 simply because it's the only practical option. Performance should be approximately the same as method 2 anyway.
Yes.
Develop games in your browser. Powerful, performant & highly capable.
Microphone input should be coming eventually to HTML5, at least on Chromium based platforms (Chrome + node-webkit). Last I tested it I couldn't get it working, but hopefully the kinks will be worked out soon.
Construct 2 doesn't support writing files at the moment. Your best bet is either WebStorage or savegames.