What does "the heck" mean?

What does "heights" mean here? Should I always put "s" to use like this meaning?

Yes, in this type of context, "heights" should always appear in the plural form. The speaker has used "heights" to refer to the state of being high up, like in the sky or on a high building. This is why the full expression is "fear of heights." Ex: I have a fear of heights. Ex: I'm not scared of heights. I've even gone bungee jumping and sky diving.

What's the difference from "I will be a good husband"?

The difference between these two sentences is in the words "would" and "will". "I would make/be a good husband" is less direct and implies that he doesn't know for sure if he will become her husband. On the other hand, "will" is very direct. If you say, "I will make/be a good husband", this implies that he is certain that he will become her husband. This is generally true with all uses of "would" and "will". "Would" is often more polite to use and common to use if you are not certain of something.

What does "set someone up" mean here?

"(To) be set up" is an informal expression which is usually used to mean two things: to be framed for something (like when someone secretly plans for your failure) or to be matched up with someone in a romantic manner. This clip is an example of the second meaning. The speaker can be understood as saying, "if your mom does set you up (matches you up with someone), just think of it as good dating practice." Ex: My mom set me up on a blind date. It turned out to be my childhood best friend! Ex: My mom loves to play matchmaker. She has tried to set me up so many times.

Is "good at" used a lot? Please teach me some example sentences.

Yes. The phrase "good at" is used quite frequently in English. You can either say that someone is good at something or not good at something. If you are good at something, it means you do that activity or task well. If you are not good at something, it means that you struggle with that activity or task. In this movie, Bradley Cooper's character tells Lady Gaga that he can't keep secrets (I'm not good at keeping secrets). Here are a few example sentences. Ex: Wow! You are really good at sewing. Ex: I'm not very good at math. Ex: Lady Gaga is good at singing. Ex: He is not good at telling the truth.

What does "it's like" mean at the beginning? Is it a filler word?

"Like" in this case is used to mean similar to or express resemblance. So the sentence "it's like I always say" here means "similar to what I always say". Here's a few examples of "like" expressing similarity: Ex: Listen to this song! It's like that song we heard yesterday. Ex: You are just like your dad.