Learn English – what is the difference between ” when it rains” and “when it is going to rain”

The present continuous, and not the simple present, is called for in both of these sentences.

We use the present continuous (or present progressive) to talk about events or conditions that are in progress or unfinished at the time of speaking. We use the simple present to talk about events or conditions that take place in general.

When we say "It rains", we say only that rain falls, without any reference to the time of the event. When we say "It is raining", we say that the rain falls as we speak.

Thus, the present continuous is correct in your first sentence:

It is raining, why don't you take your umbrella?

It is sensible to take the umbrella if the rain is in progress at the time of speaking. If the undeniable fact that "it rains" were a plausible reason to carry an umbrella, everyone would carry an umbrella every moment of every day!

In your second sentence, the same principle applies. When we say "You wait", we say only that the subject waits, without any reference to time. When we say "You are waiting" (or, with subject–auxiliary inversion in the interrogative form, "Are you waiting"), we say that the person waits at the moment when we speak.

Thus, the present continuous is also correct in your second sentence:

Who are you waiting for?

My umbrella is borrowed by Tom.

Isn't exactly wrong, but it doesn't sound natural. The umbrella is in a state of having been borrowed.

My umbrella has been borrowed by Tom.

Sounds better but still kind of stiff. This is talking about the act of borrowing, being in the past, with emphasis on the umbrella as the thing being borrowed rather than on Tom doing the borrowing.

My umbrella was borrowed by Tom.

This is how I would phrase it if I wanted to use the passive voice. I might use this if I want to emphasize the umbrella over Tom. The meaning in this situation is the effectively same as "has borrowed" but it sounds better. In other situations though "was" and "has been" have different meanings.

Tom borrowed my umbrella.

Using the active voice, this is what I would normally say as a native speaker. Emphasis here is on Tom doing the borrowing, but the reason I'd say it this way is just that the active voice "sounds better" than the passive voice.