Yes(i)If x.y in R* then we have x.y not equal to 0 implies that x is nonzero and y is nonzero. So, the statement is true

Well means there is such that The multiplication in a ring is associative; so what can you deduce from these equalities?(ii)I think this statement is false but I dont know how to prove it

Try to see what happens if you take(iii)This part I dont know