"Are you hearing me" Vs. "Do you hear me"?

Question

When I learnt English grammar I was told that some of the senses don't get "ing" of present continuous, therefore we should say "I see it now" rather than "I'm seeing it now". On the same logic, "I hear you now" rather than "I am hearing you now". But I doubt it in practice. I want to talk freely but at the same time to be sounded natural. When should people keep the mentioned rules in practice, if any?

For example: Imagine a teacher in a lecture who doesn't(?) hear his student while he ask him question. Should he tell him:

I am sorry, I don't hear you, so please, speak a little bit loudly.

or

I am sorry, I am not hearing you, so please, speak a little bit loudly.

Kindly, inform me if there should be a difference between formal and informal language in this case.

Answer 1

In that specific context, we'd actually say, "I can't hear you," since we know "you" are speaking. "I don't hear" may indicate that there is no sound to be heard: I don't hear anyone out there.

In general, both the simple present and the present progressive forms of sense verbs are used. Often the difference between them is only the difference you'd expect from the tenses - one (progressive) describes an ongoing event, the other (simple present) a habit, or an event that's not time-bound:

Do you see that? // Are you seeing this?
If I hear you say... // If I'm hearing you correctly...
She feels the soft grass // The kids are feeling the animals in the touch tank
The cook smells the soup // While the dog is smelling all the other dogs...
He tastes cardamom in the coffee // As the diners are eating, they're tasting all the flavors in the food

Answer 2

It is true that usually the sense verbs are used in present simple when describing a present situation. The verbs see and hear are stative verbs, and when using them, present simple is natural and correct.

The "-ing" form is more often used with these verbs as a gerund, which is a description of the activity. For example

I enjoy hearing her voice

I miss seeing the ocean

Present continuous can be used to emphasize the repetitive aspect of an experience:

In every electoral campaign, we are hearing the same arguments.

In the example you provided, the teacher refers to a one-time situation, so he should use present simple. Typically he would say

I can't hear you, can you please speak up?

But if it's a repeated experience, he could use the continuous:

I'm not hearing people who are sitting in the back of the room. Can you please come to the front rows?

A more detailed discussion of present continuous with stative verbs can be found here.