What exactly is affected by a higher view-distance on the server side?

Solution 1:

From the Minecraft wiki, the view-distance attribute in server.properties means:

Sets the amount of world data the server sends the client, measured in chunks in each direction of the player (radius, not diameter). It determines the server-side viewing distance. (see Render distance) 10 is the default/recommended. If you have major lag, reduce this value.

In other words, the server will always send the player a certain amount of chunks, determined by that value (by the way, that value can be between 3-15). The client can decide what to do with it: load it, or disregard it.

Now, about what chunks are loaded. Wheat grows when its chunks are loaded. The Minecraft Wiki says (got this quote from this answer):

In multiplayer mode, a grid with a default radius of 10 (for a total of 21x21 or 441 chunks) is loaded around each player and sent to the player by default, although this radius can be configured to be between 3 and 15, usually only lowered with a poor connection home server. These chunks may have activity (mobs spawning, trees growing, water flowing, dropped items disappearing etc.)

The value they talk about - 3 to 15 - is the view-distance attribute. This means that the number of chunks said is loaded around the player at any given moment.

Just to answer that 32 view distance question, a believe Minecraft will send you the view distance to be 15, instead of 32, because 15 is the max value.

Note: 15 may not be the max value anymore, as indicated by @TrudleR