[Win,odd Dhamnekar]

 1] Is following Lewis dot structure of SO₃ wrong? If wrong, why? please explain.

2] Chlorine is used to purify drinking water. Excess of chlorine is harmful. The excess of chlorine is removed by treating with sulphur dioxide. Present a balanced equation for this redox change taking place in water.
 The given redox reaction can be represented as:
Cl₂(s) +SO₂(aq) + H₂O(l)  Cl^-(aq) + SO₄^2-

Now in the above reaction, if we show on the product side SO₃ and balance this  redox reaction, is that correct, useful and practical?

If we use SO₃ on the product side of the above-mentioned redox reaction, the net reaction would be as follows:
Cl₂(s) + SO₂(aq) +H₂O(l) 2Cl^-(aq) + SO₃(aq) +2H⁺

[Win,odd Dhamnekar]

1] Is following Lewis dot structure of SO₃ wrong? If wrong, why? please explain.

2] Chlorine is used to purify drinking water. Excess of chlorine is harmful. The excess of chlorine is removed by treating with sulphur dioxide. Present a balanced equation for this redox change taking place in water.
 The given redox reaction can be represented as:
Cl₂(s) +SO₂(aq) + H₂O(l)  Cl^-(aq) + SO₄^2-

Now in the above reaction, if we show on the product side SO₃ and balance this  redox reaction, is that correct, useful and practical?

If we use SO₃ on the product side of the above-mentioned redox reaction, the net reaction would be as follows:
Cl₂(s) + SO₂(aq) +H₂O(l) 2Cl^-(aq) + SO₃(aq) +2H⁺

 If there is SO₄^2- on the product side of the unbalanced redox equation, then the net reaction would be as follows:
Cl₂(s) + SO₂(aq) +2H₂O(l)  2Cl^-(aq) + SO₄^2-(aq) +4H⁺

Are both reactions practical?

[AWK]

SO3 (aq) is nonsense. You go back to the time when acid anhydrides were considered acids, about 200 years ago.
When asked about your reaction

Cl2(s) + SO2(aq) +2H2O(l)  2Cl-(aq) + SO42-(aq) +4H+

you answered yourself earlier - purification of drinking water.