Forever: you can say (in) perpetuum or in aeternum (all the time, eternally,"for eternity", forever...). Also perpetuo, sempiterne = perpetually, continually... Sine fine = without end...
Aeternaliter doesn't appear in my papar dictionary, I found that in my other dictionary. Some quick searching on the Lewis & Short (http://www.latin-dictionary.net/definition/2099/aeternaliter)says that it is a late classical period word. The ending -ter is an adverbial ending. However, paper dictionary shows that both aeterno and aeternum are also adverbs that mean the same thing. Aeternaliter seems to be needless to me. You can use either aeternum and aeterno to mean the same thing and it is less letters. But if you want to use aeternaliter then I think it should be good.
Adverbs don't express gender, so those words are fine for any gender.