Q.1: You can not check out the source code for browsers like IE(the most popular browser), because they are not publicly avaliable. You may however, check out the source code of some open source broswers. In that case, you better check out the respective forum of each browser or contact the authors of that browser.
Q2: The browser's color rendering capability primarily depends on the monitor. 8-bit monitors are limited to displaying 256 colors, and the system software and browsers reserve up to 40 colors for their own use (256-40=216). However, a latest monitor can display up to 16,777,216 colors and so are the browser running on those monitors.
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Dust fills my eyes / Clouds roll by / and I roll with them / Centuries cry / Orders fly / and I fall again
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