Your problems in parts 1 and 2 - reflexivity and symmetricity (is that a word?) - are easily resolved if you remember that . In the first one, take , and in the second remember that .
For the 3rd part note that the value of does not matter, as long as some exists. Thus, you have shown that the in this instance is actually just .
For instance, if we take the equivalence class of all numbers of the form , clearly so . Also, so . Further, so , and also so . Then, so .
So we have an example of symmetricity and transitivity.