Does Russian make any distinction between the simple and progressive aspects? I.e., is there any way to distinguish in Russian between "Her children go home" and "Her children are going home"?
Her children go home can be translated Ее дети ходят домой. It'd be imperfective form of ходить and wouldn't be making any sense.
Домой is an adverb, roughly translates as 'homewards'. Дом is just home, a noun.
Think of the difference in saying 'I am going home' vs 'I am going to home.'
дети is an odd word. It only seems to have a plural form. As a plural word, in the way I've encountered it so far, gender is irrelevant, it seems, because all the articles and possessive pronouns use one form for plurals. So far, that is.
I have not been able to find a singular version of дети, and thus can't figure out what gender it is, if it has one. I also don't know how you'd figure out the ending for other cases.
The singular of дети is ребёнок. Both ребёнок and дети are male. The singular of дети used to be дитя́, and the plural of ребёнок used to be ребя́та. As far as I can tell, you will only find those forms in poetic speech or dated texts (I'm new to Russian, please correct me if I'm wrong!)
If you happen to use Windows 10, there's a Russian keyboard available where the russian alphabet is placed just like an English keyboard, and letters like ya (я), yo (ё), yu (ю), sh (ш), ch (ч) etc are made simply by pressing these letters (press y + o for ё for example), it makes it much easier to type your answers.
"ё" is on the left of "1" key, under "ESC" key.
That's the standard Russian layout. If you are using Russian typewriter layout then the "ё" is between "right shift key" and "ю".
My keyboard has ё mapped to the ~ key (above tab). Hopefully that works for you.
Sharing a tip I was given: hold down the е for a little longer. Also changes ь to ъ.