I'm a bit surprised 'home' was accepted. That would translate 'Heim,' but not so much 'Wohnung.' It's not an accurate translation. Probably it's because there isn't an English equivalent covering the full meaning of 'Wohnung,' which spans 'flat/apartment' and 'residence' or 'living place,' with the more common sense being 'flat/apartment,' and 'home' sounds more natural or casual than does, say 'residence,' fitting with the casual use of 'Wohnung.'
In instances like this it is useful to keep in mind that the DL system is drawing on a limited number of "acceptable" options programmed into its database. That DL rejects 'residence' as Eng. translation, does not mean that it's wrong. Unless the specific type of 'Wohnung' is known or implied, just about any kind of dwelling can be called 'eine Wohnung'. http://www.dict.cc/?s=Wohnung
Nein. It's Meine because it's feminine
Here's how it works...
In nominative, masculine and neuter nouns are preceded by mein (or dein, sein, etc.), while feminine and plurals are preceded my meine. In accusative, masculine nouns are preceded by meinen, neuter ones by mein, and feminine/plurals by meine.
See here for an overview of German pronouns by case (nom. acc, etc.) and person (my, your, his, her, etc.). You'll see that if it's alone you have a different set. Das ist mein Buch, das Buch ist meins!
I hope this helps!