I don't get which part of this sentence is referring to an apology.

When can I use "I will be heard"?

"I will be heard" can be used when you are upset, angry or feel as though someone is not listening to you. It's not the most common expression but it is used occasionally. For this video, it may have been added for humor purposes. Ex: Listen to me! I will be heard! Ex: I will be heard! This is not the last time you hear from me.

What does “thanks to someone or something” mean?

The expression "thanks to" someone means because of or due to someone, the situation happened. In this case, it can be used to express gratitude towards this person. Ex: Thanks to my brother who picked us up, we didn't have to walk there. Ex: Thanks to her help, we got the project done on time. However this expression can also be used to express negative feelings towards someone or something for causing something to happen. Ex: Thanks to the stock market crash, we all lost our jobs. Ex: We were late thanks to you.

What does "sick" mean here?

"Sick" in this case is used to describe someone who is perverted or who has inappropriate, unusual, or disturbing tendencies. It can also be used in this case to refer to someone who has a mental disorder. Ex: He is a psychopath with very sick ideas. Ex: He is a sick man; don't let your children anywhere near him.

I don't get which part of this sentence is referring to an apology.

"Crawl back" is an idiom that refers to someone admitting they were wrong and asking for forgiveness, and they do this by apologizing. Ex: My friend crawled back today after he started a fight with me yesterday. Ex: Her ex-boyfriend tried to crawl back, but she wouldn't get back together with him.

Is the phrase "smell a rat" commonly used?

"I smell a rat" is used to express that one suspects trickery or deception. It's also used to express that you believe someone is being dishonest or secretly causing harm, as "rat" is slang used to describe someone that has betrayed or cheated someone else. Ex: Our secret recipe got leaked to our competitor. I smell a rat. Ex: The engineer was suspected of being a rat by his coworkers.