can I use windows 8 font （Segoe UI）for my web app?

will help you This is from Microsoft's own stylesheet for Windows 8 (Metro) apps:

/*
Explicitly define a Segoe UI font-family so that we can assign Segoe UI 
Semilight to an appropriate font-weight.
*/
@font-face {
    font-family: "Segoe UI";
    font-weight: 200;
    src: local("Segoe UI Light");
}
@font-face {
    font-family: "Segoe UI";
    font-weight: 300;
    src: local("Segoe UI Semilight");
}
@font-face {
    font-family: "Segoe UI";
    font-weight: 400;
    src: local("Segoe UI");
}
@font-face {
    font-family: "Segoe UI";
    font-weight: 600;
    src: local("Segoe UI Semibold");
}
@font-face {
    font-family: "Segoe UI";
    font-weight: 700;
    src: local("Segoe UI Bold");
}
@font-face {
    font-family: "Segoe UI";
    font-style: italic;
    font-weight: 400;
    src: local("Segoe UI Italic");
}
@font-face {
    font-family: "Segoe UI";
    font-style: italic;
    font-weight: 700;
    src: local("Segoe UI Bold Italic");
}

@font-face {
    font-family: 'ChunkFiveRegular;
    src: url('whatever source');
    font-weight: normal;
    font-style: normal;
}

around this issue You can't license Segoe UI from Microsoft without direct contact, you can license the mono font from Ascender Corp who are linked to from Microsoft webpage for Segoe UI, however it is not the same as Segoe UI.
I would suggest Open Sans as an alternative to the Segoe UI font, it is quite similar and has much more open licensing for using as webfont (that link is actually to Google's hosted version of the font) - So you could have Segoe as the main font then fall back to Open Sans on non Windows 7+ Systems.

around this issue This error is coming from within the content processor. For some reason, that font isn't supported by the internal GetCharacterSpacing method that is used to figure out how wide the characters are.
(To wildly guess at the cause: maybe the 2012 build process is using a newer version of the .NET framework - eg: 4.5 vs 4.0 - and that particular method doesn't work the same between versions for some crazy reason. You could maybe mess about with MSBuild - but that's way too much effort.)

seems to work fine How can I change it so that any button I create for my Windows 8 app has a differently-colored Segoe UI glyph than the default (white)? I tried the following to no avail: , Use Foreground property.

<Button Style="{StaticResource AppBarButtonStyle}" Foreground="Red"
        AutomationProperties.Name="Button" Content="&#xE17F;" />

it fixes the issue GDI does not support color fonts (even if you go the full Uniscribe route), you have to use Direct2D if you want color font support. It makes sense that the simpler GDI APIs don't support color fonts as color fonts require using OpenType tags and none of DrawText/TextOut provide that level of control, Uniscribe allows for such tags but has simply not been extended to support color fonts.