How to install full Unicode fonts The page http://de.m.wikipedia.org/wiki/Hammurapi contains
several occurrences of the character Ḫ (1E2A;LATIN CAPITAL LETTER H WITH BREVE BELOW), http://codepoints.net/U+1E2A which does not display on Galaxy S3. Neither with the built-in browser, nor Chrome, nor Miniopera.

Similarly, ẞ, Capital Sharp S, http://codepoints.net/U+1E9E cannot be displayed.

Does Android support full Unicode? How can I install full Unicode support?

Edit: I have (so far) not modified anything at all.
As t0mm13b had said, Android as a framework does support Unicode. As you are probably aware the vanilla Android is as such available as a stock option only to Google's own devices (The Nexus series). Other Android devices will have some sort of topping layer over this vanilla layers. This topping layer will usually be cosmetic changes by the manufacturer like HTC Sense UI etc. 

Even if there are no such topping layer, the manufacturers compile the source of vanilla ROM with suitable drivers of their devices and add slight country specific enhancements. 

Take a look at a similar question that I had asked which is not very different from what you had asked, if the language specific features and names are not accounted. That question explains how an Android device displays a glyph (not characters) on screen and the software components that are involved in that process.

To put it in a nut shell, to display a character Android requires a suitable font file and a rendering engine. Absence of former could result in a rectangular box and later will result in improper display of glyph.

In your case the ROM that your S3 has might not have the above said.  Try to test with the devices that does display it (probably in some other region, the S3 might display it properly) and find what font files differs between yours and theirs.