So why are there two different words for child and children (plural)? Is it just a quirk? I would expect the plural of children to be робёноки (children) or something, or maybe the singular of this version of children to be дет or деть (child).
I'm just curious, can I use either or? Or how does this work?
No reason, really. It is called suppletion. The phenomenon is found in many languages. For example, in English "went" works as the past tense of "go", and "people" effectively works as a plural of "person" (whereas "persons" enjoys limited use).
«Дитя» is rarely used these days unless you go for high style—but its plural is used as a de facto plural of «ребёнок».
«Ребята» is the plural you might use when talking about boys or addressing a group of kids to tell them something.
ive found the app lingvist is really useful for learning cases.. its like fill in the blanks. it tells you what case its expecting, and if you type the wrong one it shows you a table of all the diff declensions for single/plural/perfective/gender etc... unfortunately its limited to only 80 cards/day w/o premium or something
On the e. Useful tip: Plug the word in question in here: http://starling.rinet.ru/cgi-bin/morphque.cgi?flags=endnnnnp
It will show all the forms of the word and the stress. Always read the entire table and you'll start to figure out the rules.
Тебя = you (Genitive case) Меня = I (Genitive case)
You are correct in that both are used in the same manner. If this does not yet make any sense, fret not, this will come. In the meantime, have a beautifully useful link, first provided to us by Theron, where you can input any Russian word you are uncertain about and have a look at the declensions.