"I am going home."
Translation:Я иду домой.
That would mean I am going home by some sort of transport, not necessarily implied by the English.
I've also heard this without any motion verb, but it wasn't accepted. Any thoughts on that folks?
yep, "я домой" is an informal, conversational way of saying "I'm heading home," and propably isn't acceptable because it is only used conversationally and never in written form
No. The dative form of дом is дому. Домой is an adverb of direction (i.e. it means "towards home"). Home as location (at home) is translated into another adverb - дОма.
We use «дом» for any home, house or block of apartments when the word is the subject or predicate in a sentence or a direct object of a verb, or when it follows a preposition which requires putting the noun in the accusative case. Here are a few examples: «Мой дом - твой дом», «Вот наш дом», «Я вижу дом», «она вошла в дом», «змея заползла под дом», «он завернул за дом», «мы говорим про дом», «волна высотой с дом», «дерево упало на дом». In «задавать на дом» (“to give homework”) and «задание на дом» (“[assigned] homework”) «на дом» is pronounced as “nud ‘em”.
Yes. Я хожу домой means I go home (on foot) every now and then. The Russian sentence looks incomplete. For example, you can say Я хожу домой пешком = I walk home or Я хожу домой обедать = I (usually) go home for lunch. Ходить, ездить, летать, ползать, плавать etc refer to habitual actions or back-and-forth movements or movements all over a particular place (in the latter case they are followed by a noun with the preposition по), whereas идти, лететь, ползти, плыть еtc. refer to actions in progress and, if used in their literal meaning, to movements in a particular direction.
Use «иду» for “I am going/walking”, «идёшь» for “you are (informal singular you) going/walking” and «идёт» for “He/she/it is going/walking”. Google for “Russian verb conjugation” for more details.