It looks like you figured out the answer to the first question, but GT is the second game in the series, so yes, they're related, and you can transfer some information via the DataCrystal file. It's not required, but you will potentially miss out on a scene, and more in future games. Endings of GT are not effected.
Also, try not to double post: you can edit your posts if you thing of something else you'd like to add.