From a research standpoint, if you repeat old work and get the same result, then you haven't advanced the state of knowledge and so probably won't be able to publish anything more than a note.
One exception would be confirming an older result but with a completely different methodology. Then it is the new methodology that is the "new and exciting" part that might merit publication.
But, especially in the medical field, if you repeat old work and show that the original work was wrong, or even dangerous, then you have something worth publishing and can become famous (or infamous if you are wrong). But I think that as a student, you should undertake such work only if you have a strong suspicion and some evidence that the original is in error. Otherwise you won't gain much from just following other's footsteps.
So, in general, it is probably better to work on untrod ground, on something new, as hard as that can be. The fact that your advisor gives you a lot of freedom is good, but only provided that they also give you guidance on your ideas and also provide some worthwhile ideas for you to follow.
I'm not sure what you mean by your question on citations, but it is typical to do a "literature survey" before you start on a new research direction to make sure you know what is known about the topic. If things are already known (likely), you will cite them if you build on them in any way.