You can. Putting, say, #Funny in your antenna will show you everything with the keyword “#Funny”. This is more powerful than just hashtag following, as you can even follow specific words.
Alas, as you mentioned, antenna content doesn’t show up in the home feed yet. I believe there is an open issue to change that.
I’m fairly certain they combined Instagram DMs and FB Messenger into one thing a couple of years ago. Instagram DM is now just FB Messenger but in the Instagram app, and its chats can be viewed and interacted with fully from Messenger.