Welcome!

You can definitely play ARR itself without Heavensward, as the expansion pack storyline and content only becomes available after completing all the ARR story quests (and there is a lot of ARR content to play through to reach that point). The only thing really you will miss out on at the start is being able to create a character of the au ra race which requires Heavensward to be purchased and registered to your account.

Other than that, you'll have the entire ARR game on it's own to play through and all it's content to last you until you are ready to purchase Heavensward, so don't feel you are missing out not having it straight away.

As for the 30 days free, I'm not sure how that works with the free trial version, my understanding is that it automatically occurs once you upgrade the trial to a proper account, but someone more knowledgeable on that subject would be able to answer that better than I can.