"She loves her husband."
Translation:Она любит своего мужа.
Is муж declined into мужа because it's accusative for a masculine animate object, right?
Yes, you're right.
Also, why does своего translate into "her"?
«Своего» means the possessor is the same as the subject of the sentence. So, «Я люблю́ своего́ мужа» would be translated 'I love my husband.'
Isn't the его particle for masculine?
We don't generally use его, её, мой, твой, etc., when we can use свой.
does the "его" in "своего" have anything to do with "его" (his)?
No, these are completely different forms. -его is an adjectival ending (alongside with -ого), and его is a pronoun.
And why is it "своего" instead of "свой"?
«Своӣ» is the nominative case, it's used for a subject... Well, except that it's not: you never have «свой» in the nominative case, because the nominative case is for subjects, and «свой» means 'possessed by the subject', and it makes little sense to say it's possessed by itself. So «свой» is only used as an accusative case for inanimate nouns.
«Своего́» is genitive and accusative for animate nouns.
Х and Ж are very different letters. :)
Муха means 'a fly', мужа is an accusative case of муж 'husband'.
Normally 'муха' is be a feminine word (so it should be она любит свою муху 'she loves her fly'), and you've used it as a masculine word мух. But sometimes we can change the word's gender. For example, we can do it in fairy tales when a fly is a protagonist. So, your sentence means that she loves her fly, which is a very important he-fly. :)
I never used the word Supruga (forgive me if transliterated/spelled incorrect.). Any insight on it?
Супру́га is like 'spose' (but, unlike the English word, it's feminine-only; it's masculine counterpart is супру́г), it's more formal than жена́.