If I were standing on the surface of the sun, how far could I see? Assuming it would be possible to handle the intense heat... Is the surface even? If not, would average surface elevation be an appropriate definition of "surface"?Does the sun have an atmosphere that would degrade visibility? How far apart are small solar flares that would block the horizon? What affect would the heat have on the light rays?
Assume I am 2 meters tall.
 A: Given that the sun regularly ejects plasma clumps kilometers long, or that "sunspots" are storms larger than the Earth's diameter, you may want to adjust your question :-).
The wikipedia page, http://en.wikipedia.org/wiki/Sun#Characteristics , gives a good description of the core, the plasma layer, the so-called atmospheric layer, and so on. If you dig into this info I suspect you'll find there is really no "surface" with any stable structure.  
To answer the last question: "heat" is related to temperature, and photons are unaffected by temperature other than the chance that they'll interact with (or be emitted by) highly energetic particles.
A: "If I were standing on the surface of the sun, how far could I see?"
Exactly the same distance as if you were standing on any other celestial body. Look up, the cosmic event horizon is about 14 billion parsecs away.
"If I were standing on the surface of the sun, how far away is the horizon?"
In theory, about 52km, assuming you survive the heat, gravity etc. and don't mind washing up and down in the surging plasma making up the surface. Any ejections or flares would be localized and transient. Also assuming it's a clear day.
"If I were standing on the surface of a sun-sized hollow sphere, how far away is the horizon?"
The horizon of the mini-Dyson's sphere would be about 52km away.
A: According to Opacity of an Ionized Gas, "light from regions [of the sun] where the pressure is greater than 0.01 atm. is cut off completely, so that all we see comes from a spherical shell of rarefied gas".  
There is no real surface of the Sun.  Instead, the density and pressure of gas/plasma progressively increase from an infinitesimal value far from the Sun, to a very high value in the core of the Sun.  If you flew at a level where the pressure is similar to atmospheric pressure of the Earth, you could not see anything (except light emitted from your immediate vicinity), according the the above statement.
See table 2-1 of The Photosphere for quantitative information on the opacity of the sun at different height.  Only at a height in the sun's atmosphere where density is ~$1/10000$ of Earth's at sea level is a photon more likely than not to have a free path out of the sun without being scatterred or absorbed. 
