What is goody-two-shoes?

I don't know why the "-ing" form(starting) is used, not the infinitive(start).

"Starting" here is used as a gerund, which is a word that ends in the "[verb]-ing" form but acts like a noun. You can use this form when you want to speak about things generally, but perhaps the action (verb) you want to speak about does not have a noun form. An alternative for "there are advantages to starting early" would be "there are advantages [for] when you start early." Ex: I'm a huge hiking fan. Ex: There are many advantages to learning how to cook.

Can I use "postpone" instead of "delay" here?

These words actually have different meanings. When something has been "postponed," it means that it has been pushed back or rescheduled for another time in the future. Meanwhile, to be "delayed" means that something wasn't able to start on time/started late due to a conflict, condition, or situation. So while they are somewhat related in idea, they are used differently. Ex: Let's postpone our meeting to next Wednesday. Ex: The concert was delayed for 10 minutes.

Can I use the word "marry" to animals as well?

No, it is not generally correct to use the word "marry" for animals, since animals don't get married like humans. In the context of the video, they use the word "marry" since this story is fictional and not reality.

What is the "American Civil War?"

The American Civil War was a civil war (fought between citizens of the same country) that took place in the United States from 1861 to 1865. It was fought between the Union and the Confederacy (a collection of Southern states that chose to secede), mainly over the issue of slavery. The Confederacy wanted to keep slavery as an institution, as they benefited most from Black slave labor in their large plantations in the south. Comparatively, the Union consisted of well-established manufacturing and other industries. Other causes for the war included disagreements over state rights and national expansion towards the west.

What does "tinder" mean in this video?

"Tinder" in this context is the name of a popular app for online dating that started in the United States but is now popular worldwide.