アメリカが懐かしい, I would say is a good "I miss America," although you could be more direct with アメリカに帰りたい if you really want to go back.
I can only think of 犬に会いたい or 愛犬に会いたい for "I miss my dog," but I'm not sure that you really 会う animals. I'm not really sure what you would say for that.
To focus on "now" put an 今 in there, but I find it a bit strange (not that I'm necessarily right).