Hello Vir, 

Your third example, "on the contrary", is more typically used for opinions rather than stated facts. I would instead write, "I studied to be a teacher; in contrast, my sister is studying law."

We frequently put a comma before the conjunction as well, but usually only when the two clauses are independent.

I´m studing conjunctions in English

- I'm cooking while you are washing the dishes
- John is working while you are watching TV
- I studied to be a teacher; in contrast, my sister is studying law
- I would want to be a teacher, instead I'm working in have another job
- I don't want to go to this party, unless you come with me
- I need my umbrella whenever it's rainning
- I'm waiting at home, until you come back there
- In spite of they are Despite being tired, they will go to your party
- She wants to buy a car, however she hasnt got doesn't have enough money
- I will help you, as soon as I finish my meal
- I haven't seen my sister since she went to Italy

I´m studing conjunctions in English

- I´m cooking while you are washing the dishes
- John is working and you are watching TV
- I considered to be a teacher, on the contrary, my sis is studying law 
-I would desire to be a teacher instead I'm working at some other business
- I don´t want to go to this party, unless you come with me
- I needed my umbrella whenever It´s rainning
- I'm waiting at home until you get back thither
- In spite of they are sapped, they will get to your party
- She desires to purchase a car, nevertheless, she hasn't got enough money 
- I help you as soon as I finish my meal
- I haven´t seen my sister since she went to Italy