Yo soy, and Soy are both correct. Yo means "I" and Soy means "I am." It is redundant to say Yo soy - but it is perfectly correct. The language allows either one.
When deciding whether or not to use "un" or "una" you should determine the gender of the noun. In this case it is "boy."
if "niño" means "child" rather than boy, then who can tell me how to say "boy" in Spanish? Do those two words differ?
"niño" means "boy" and also "child" (typically male). There is no fully gender neutral word in Spanish for a child.
Yo sounds like "jo", correct? That's what I'm hearing; is the y sound pronounced like a j?
It depends on the country. It varies all the way from "y" to "j" to "sh". You can stick with "y" though.
pronouncing the words like 'un' or 'una', since we begin to learn the words by mentally pronouncing them and they get established in mind. Is it the 'un' in 'unless' etc, or, as in 'moon'?
Would a female child ever use this sentence to say, literally, "I am a child?"
They would say "Yo soy una niña".
So "niña" and "niño" both mean child?
Yes, "niño" is male child (or "boy") and "niña" is female child (or girl).