To be clear, modals are a common construct in many Indo-European languages, such as German, French, Italian, Spanish, etc.
What makes them modal is their unique structure and semantics. Thus, in English, "I can read" becomes in German "Ich kann lesen". Generally, they modal is conjugated for person and time, with an infinitive that is not.
There are very few true modals. In English, 'can', 'may', 'wish', 'should', and a few others corresponding to 'kann', 'darf', 'will', 'sollte', etc.
It is important to be clear what are and are not modals. This is crucial since how the rest of the grammar works is different for pure modals. For example, in German, modals after 'haben' (to indicate past tense) stay as infinitives, not past participles. So, 'I have (or was) at school (been) able to read' is 'Ich habe in der Schule gelesen konnen' - NOT 'Ich habe in der Schule glesen gekonnen' or some such.
The confusion comes from the fact - when compare to all other European langauges - that the English infinitive is described as 'to read', or 'to be able', but English drops the 'to' gramatically is use ('I can read', NOT 'I can to read'. Oddly, it comes back in the past: 'I was able to read' (which is the same as 'I could read').
It makes many things, to and English speaker, unfortunately appear as modals which are not. In your example, 'Ich hoere dich husten' is not a modal at all. In fact, it is very parallel to English: 'I hear you (to) cough', though we would leave the 'to' out with it understood as an infinitive. In older times (like at the time of Shakespeare), the 'to' might have been left in.
But it does not make 'hear' a modal.