Check it again, it may be hidden

Optionally, refer to this: Build error caused by thumbs.db

Okay I just found an even better way after I stumbled upon the API of FlxG.keys:

FlxG.keys.preventDefaultKeys = [LEFT, RIGHT, UP, DOWN, SPACE];

Better way without modifying your index.html, put this in your Main.hx or anywhere in your Haxe code:

#if js
js.Browser.document.onkeydown = e -> e.preventDefault();
#end

I made a game for LD39 and there's a feedback saying that arrows key make the web page move. After a while of googling, nothing came up.

So again the question is:
How do you prevent default key events for HTML5 games?

You would need to convert all your shapes to paths for the best result and remove all effects or filters if there are any, as Lime doesn't support rendering for advanced shapes or filters and the like.

This may be late but you can try altering FlxObject.SEPARATE_BIAS
Perhaps like:

FlxObject.SEPARATE_BIAS = tileSize;

This HaxeFlixel tutorial on masking could help.

I have actually tried blend modes myself. I used a transparent sprite, of course, but found no blend mode that uses the alpha of the top layer. Then I wondered if I could have a custom blend mode so I researched shaders as HaxeFlixel supports it. According to what I have read, shaders do not know nothing at all about other sprites. So, yeah, both didn't work, at least for me.

I think you gotta do that manually. HaxeFlixel only stops drawing off-screen FlxSprite.

This should help.
I have this problem myself sometimes, randomly for no reason. It just could not access but after a while it could.

To host your HTML5 on a local server:

1. Go to your html5 bin folder which has the .html
2. Open the Command Prompt there (Shift + Right Click > Open the command window here)
3. Type in nekotools server
4. Hit Enter

Options: 
-h [domain] - set hostname
-p [port] - set port
-d [directory] - set base directory
-log [file] - set log file
-rewrite - activate pseudo mod-rewrite for smart urls

That's the first two questions.

And to answer the 4th: to detect if a user is on desktop or a phone, you will want to use FlxG.onMobile. It's been added a while ago but I guess it was not publicly noticed.