When can אנו be used instead of אנחנו?
Always - but it's formal, so it's not used in speech.
hem negdénu v-anakhnu negdám
feminine with audio: https://forum.duolingo.com/comment/17010421
נגדם vs נגדכם vs נגדך
I am having a hard time knowing when to use which. Can anyone offer some pointers?
ll נגדך = against you (singular masculine/feminine; they're written the same but pronounced differently). נגדכם = against you (plural masculine). נגדם = against them (masculine).
Full inflection here