Does the word "on" means to start something?

Is "start" necessary here?

No, "start" is not really necessary in this case. "Start" is just used here to emphasize that she isn't already crumbling, but she must continue to avoid crumbling. However if you omitted "start" in this sentence, the sentence would have the same overall meaning. But you should also know that the word "crumble" is not a very common word to use in this case. "Crumble" here has the same meaning as "break apart", but it is mostly used for things which physically break apart into pieces.

What is the meaning when speaker says “What + adjective + noun”?

When someone says "What + adjective + noun", they are making an exclamation about the noun they are describing with the adjective. In other words, "what" is used for emphasis when saying the adjective + noun Ex: What horrible weather! Ex: What pretty shoes!

What's "already" mean here? I don't usually see "already" used at the end of the sentence.

Great question! "Already" is used in this sentence to express more surprise or show more emphasis. We raise our voice at the end when we say "already" to express the feeling of being surprised. Ex: I told you the secret already! Ex: Is she drunk already?

What's "make contact with" mean?

To "make contact with" someone means you find out where they are and meet, talk, or write to them. Ex: We went hiking in the mountains and only made contact with other people after three days. Ex: After he left, he tried to make contact with her, but she didn't want to talk to him ever again.

What does "diamond rich" mean?

"Diamond-rich" is just another way of saying "rich in diamonds." Dua Lipa doesn't mean this literally, she has used this expression to state that the feeling her lover gives her is like feeling rich, or feeling fantastic. It is a metaphorical expression meant to express the intense emotions she feels. However, "[noun]-rich" is used to express that someone is "rich" in or has a lot of something. Ex: She's diamond-rich. She has over ten rings that are more than one carat. Ex: He's real estate-rich. He has over ten investment homes.