(1) How many English words begin with s but are pronounced as an sh? I know of three -- sure, sugar, and the name Sean. Are there any others?
(2) Where, why, and when did the letter c take on an s sound? The letter is derived from the Greek gamma, which phonetically (voiced hard g (as in Phoenician or Hebrew)or voiceless k)) is nowhere close to an s sound
1. Other than the three you mention, the only English word I know of in which initial <s> spells [sh] is sumac, which has a more common pronunciation with [s].
2. In Old English <c> regularly spelled [k]. But over time when it was followed by <e>, <i>, or <y>, the sound it spelled changed to [ch]. This change had taken place by the 10th century. Also, later, during the Middle English period the Norman French scribes used <c> also to spell [k], but before <e>, <i>, or <y> the original French sound had changed to [ts]. In time the [ts] eased to [s].
So our distinction between hard and soft <c> comes from both the Germanic side of the language family tree (via the Old English [k] vs. [ch]) and the Romance side (via the Norman French [k] vs. [ts]). Another way of symbolizing the sound [ch] is [tsh], which better suggests the similarity between the French [ts] and the Old English [tsh].
This distinction arose from the influence of the vowel sound following the <c> upon the pronunciation of the consonant sound spelled by the <c>. You can experience some of the pressure leading to the distinction if you compare the way you pronounce the [k] sounds in, say, kit and cot: In kit you should feel the [k] being pronounced further forward in your mouth, in cot further back. The difference arises because while pronouncing the back [k], your mouth gets itself set to pronounce the upcoming vowel: in kit that vowel is [i], which is pronounced toward the front of your mouth, so your tongue begins to move forward while pronouncing that [k]. In cot the vowel [o] is pronounced towards the back of your mouth, so your tongue stays back while pronouncing the [k]. Over the centuries this modest difference in the pronunciation of the [k] increased to our current distinction between hard and soft <c>, [k] and [s] – roughly, from [k] to [ts] or [tsh] to [s].