Could you please tell me if the following verbs can take the -ing form in the examples below? I included a sentence I need to write in an email.

1) I'm smelling the perfume of the flowers.
I'm testing a red wine.
2) I'm hearing him coming (I think you can only say " I can hear him coming)
I'm thinking of going to London.
I think he won't come.
I'm thinking about my next trip to France.
3) What do you think of/about him?
You just need to give your students the class email address and they can start the email partnership.
4) Of course, my students will need to know your class eamil address to answer your students' emails. Let me have it as soon as possible.

Sometimes the "I'm hearing ... " (or whatever present progressive you're using) ends up sounding like a non-native English speaker. Here are the ones that work well:

1. OK

2. You're right ... about all of them.

3. What do you think of him? = Do you think he's good to be around? Is he silly or dangerous ... or is he OK to be around?
(To use "about" is OK, too, but the more common usage is with "of.")

Add a comma after "email address" - this is a compound sentence.

4. email -- spelling

To determine whether a verb can take the -ing form in the examples provided, we need to consider the verb's characteristics and the context in which it is used.

1) "Smelling" and "testing" are both verbs that can take the -ing form. Therefore, the examples are correct.

2) "Hearing" usually does not take the -ing form in the sense of perceiving sounds. Instead, we typically use "can hear" or "hear" by itself, as you mentioned. So, the corrected example would be: "I can hear him coming."
For the other examples, "thinking," "think," and "thinking about" can all take the -ing form. Therefore, the examples are correct.

3) Both "think of" and "think about" can be used to express opinions or considerations. Therefore, the examples are correct.

4) The sentence is mostly correct, but there is a small error. Instead of "eamil," it should be "email." Therefore, the corrected sentence would be: "Of course, my students will need to know your class email address to answer your students' emails. Let me have it as soon as possible."

To summarize, the corrections made in the examples include changing "I'm hearing him coming" to "I can hear him coming" and changing "eamil" to "email" in the last example.