Think about them that way:
0 conditional (Present Simple+Present Simple) refers to something certain and is always true. If one condition is achieved it will have consequence and there's no doubt about it.
When people turn 18, they officially come of age.
1st conditional (Present simple+Future Simple) refers to the future (thus it uses future tense). It means that if one condition is achieved it MIGHT have consequence. People have struggles differing 0 and 1st conditional. Just remember that the 0 one refers mostly to fields od science and studies. General thing is that consequences are crucial and unavoidable, which does not happen in the 1st conditional.
If she calls me, I will tell her about the party. No natural or political law is forcing me to, but I MIGHT do it.
2nd conditional (Past Simple+Future in the Past Simple"would") refers to the present. It means that if one condition was true at the moment, it would have consequences. I know, I'm explaining conditional with conditional sentence, but hear me out. This condition is not true whatsoever. Thus, the consequence is impossible to achieve.
If my dog were a cat... (but it's not; consequence is not possible now)
If I could stop the time... (but I can't; consequence is not possible now)
And this is a general idea. Remember, the 2nd conditional refers to the present! it is speaking of what the world would be if the present were changed.
3rd conditional (Past Perfect+Future in the Past Perfect"would have") refers to the past. Think about it as the 2nd conditional BUT in the past. The whole idea is the same. Now, the condition that we wanted to achieve had to be achieved in the past. There is no going back and changing it, thus there is no way of achieving the consequence.
If I had been there sooner... (but I wasn't; consequence didn't happen)
If my dog had been born a cat... (but it hadn't; consequence didn't occur)
So the 3rd conditional is just speaking of what the world would have looked like in the past if a certain condition had been achieved.
And your sentences are grammatically correct, so I hope you get the idea.