When an Uchiha member is going to get married with another Uchiha member, are they marrying their cousin? Like my question is asking, are they marrying their own cousin? I'm wondering this because I remember Obito telling Naruto that Sasuke was his relative in volume 71 chapter 683: I Dreamt the Same Dream. I also remember Madara saying the same thing to Sasuke and Obito, which got my attention.

So according to what I've read in the manga they are saying their blood is all connected which, therefore, makes them all relative? So if they are relatives that make them cousins or something like that? If they do end up being cousins, are they marrying their own cousin? Isn't that kind of disturbing to them or am I wrong and in the Uchiha there are still different family members but have the same last name, which makes them all "relatives"?
Yes, they are. They probably know it. And they aren't that closely related, anyway.

It had often been the case, historically, in noble and especially royal families to marry within the family (often to fairly close relatives) - either because marriage to a lower class was too low in status and there just wasn't much of the higher class, or simply to keep the money in the family. (A particularly silly example is the Ptolemaic dynasty of Egypt.)
It even happened in non-noble families too; somewhat famously, the maiden name of Franklin Roosevelt's wife, Eleanor Roosevelt, was also Roosevelt (she was Theodore Roosevelt's daughter), though their common ancestor was six generations away.

In the case of the Uchiha clan, it actually makes sense - they want to maximize the chance of their bloodline manifesting in the progeny. And given how large the clan is (or, at least, how large it was before Itachi wrecked it all up), chances are that, in many cases, there are quite a few generations to the nearest common ancestor.
I suspect that the Uchiha elders actually did try to make sure not to marry especially close relatives, to minimize inbreeding problems; given how crazy many of the Uchiha members ended up being... for all we know, they still failed, and the last few Uchihas did suffer from inbreeding in their ancestry.