A relation can be completely determined by its graph, which here is named and which is a set of ordered pairs such that: (I guess that most people will say that a relation and it's graph are the same thing)
For 1), for instance, a way to check wether R is a relation or not:
Reflexivity: . (i.e. aRa). That's true, thus R is reflexive.
Irreflexivity: . (i.e. no(aRa) ) It's wrong, for example (1,1) is in R.
symmetry: . That's the case.
antisymmetry: . Again, that's true (since there is no (a,b) in R with a b)
transitivity: . True, for the same reason given for antisymmetry.
(That relation is particular, it's the equality)