"Alle = all" can only be used with plural nouns (e.g. alle Kinder = all children). There are different forms of "alle" depending on the case of the noun: nominative/accusative: alle, dative: allen, genitive: aller.
"Jeder, jede, jedes = every/each" can only be used with singular nouns (e.g. jedes Kind = every child). Which form you have to use depends on the gender and case of the noun, similar to the different forms of the definite article. You can see all the possible forms here (first table on the right): http://de.wiktionary.org/wiki/jeder
Which is essentially no different than english. You wouldn't say "I want to hug all cat", you would either say "I want to hug all [the] cats" or "I want to hug every cat"
If I wanted to say "Every child likes her" would it be "Jedes Kind mag sie"? If so, how do I distinguish between "Every child likes her" and "She likes every child" when translating "Sie mag jedes Kind"? Do I do so, solely on word order?
Yes, mjondras, you are correct. 'Every child likes her.' - 'Jedes Kind mag sie.' 'She likes every child.' - 'Sie mag jedes Kind.' But be aware that the sentences look so alike because the verb is conjugated the same for "es" (das Kind) and "sie". If one of them were plural: 'She likes all the children.' - 'Sie mag alle Kinder.' 'All the children like her.' - 'Alle Kinder mögen sie.'
How do you tell the difference between She and They when it comes to "Sie"? :/
"Sie" as in "they" would use the verb without conjugating it (i.e. haben, spielen, etc.) ; "sie" as in "she" uses a conjugated verb (i.e. hat, spiele, etc.) If you research conjugating German verbs, there's a pretty general structure to how a verb is used in relation to the noun (ich habe, du hast, sie/es/er hat, Sie haben, etc.).
So in this example.. Sie mogen for they like and and Sie mag? for she likes? Thank you
That would be logical, but unfortunately, like the other modal verbs "mögen" is irregular. In the present tense singular, there is a vowel change and the first and third persons singular (I + he/she/it) get no endings.
mögen (to like)
ich mag (I like)
du magst (you [singular informal] like)
er/sie/es mag (he/she/it likes)
wir mögen (we like)
ihr mögt (you [plural informal] like)
sie/Sie mögen (they/you [formal] like)