If Binance Trust wallet could be a closed source maybe they did this because they don't want malicious people to find out how they run things which could make their wallet become a target?
It's possible, but it's guesswork. That could be the reason why the wallets are closed-source or because there is something there they don't want you to know about.
Close-source is saying trust me it's good. I promise.
Open-source is saying take a look and make up your own mind. Don't trust me just because I am telling you it's good.
If you can't see how things are running (coding) wouldn't that make it harder to attack such code or network?
Yes, but the coin has two sides. You mentioned one. The other is if someone is a security expert who understands coding, they could tell the developers what to improve based on what they see in the codebase. If there is nothing to see, no one can make corrections. And attacks could still happen with or without a public codebase.
Closed source says > we don't want you to see how we run the codes, you can target us or something
Again, it's guesswork. It can also say we don't want you to see our code because we are targeting you.
The answer is pretty simple the most popular projects are open source and they are very secure. From Linux to bitcoin core and Electrum. Everyone sees "how things are run" and they are still secure.
Open-source does not mean secure by default. Although after years of testing, improving, and probably being thoroughly put under the microscope by those with bad motives, it's pretty safe to say that the brands you mentioned are all secure. But we have also seen some open-source Ethereum smart contracts being breached and hacked for reasons that could be bad code, exit scams, lack of knowledge how to secure them properly, etc. It's very important who looks at the code and tags it as verified. If I am not wrong, some hacks occurred even though the projects were called audited and secure.