It is especially used to talk about a skill or ability in general

is the past or conditional form of can

Authorization or permission to do something

suggest a possible situation or explanation, although we do not claim that it is 100% true

indicate duty or obligation to do something;

Shall is an auxiliary modal verb that has several uses (forming the future, making suggestions and offers or to ask about them, giving orders, etc.).

It is used to recommend doing something and to state whether we think something is as it should be or not.

We use it to talk about the future when we are not very sure what is going to happen, so we say what we think will happen.

It is an auxiliary, that is, it does not have a complete meaning on its own: it needs another verb to make sense in a sentence.

It serves to express advice that we believe is morally correct.