Additions are easy. By default they are wrapped, and you can make them explicit with checked_ methods.
Assuming that you are not using much recursion, you can eliminate most of the heap related memory panics by adding limited reservation checks for dynamic data, which is allocated based on user input/external data. You should also use statically sized types whennever possible. They are also faster.
Wrapping on overflow is wrong because this is not the math we expect. As a result, errors and vulnerabilities occur (look at Linux kernel for example).
It depends on the context. Of course the result may cause vulnerabilities if the program logic in bad context depends on it. But yeah, generally I would agree.
Assuming that you are not using much recursion, you can eliminate most of the heap related memory panics by adding limited reservation checks for dynamic data, which is allocated based on user input/external data. You should also use statically sized types whennever possible. They are also faster.