about ammonia

For the chemical equations:
NH3(g) + H2O(l) → NH3(aq)
NH3(aq) + H2O(l) <==> NH4+(aq) + OH-(aq)

Question 1 :
Is the above set of chemical equations correct?

Question 2 :
How about the following equation? Is it correct? Explain it!!!! : )
NH3(aq) + H2O(l) <==> NH4OH-(aq)