I know you have figured it out by now, but I'll post the answer for anyone else with the same question.
The letter כ can make both the k and the ȟ sound. Note that at the end of the word, it appears as ך regardless of the pronunciation. The ח can only make the ȟ sound. In Modern Hebrew, both the "hard h" pronunciations are the same. Unfortunately the letters are not interchangeable, so you have to memorize which words use which one.
As far as I know, "כ", which can be pronounced two ways, only has one pronunciation when it is "ך" at the end of a word, and that is the "ch" sound like in the German "ach" or "ich" and the Scottish "loch". If anyone knows an example of when "chaf sofit" makes a "k" sound, please let me know.
They're identical nowadays, but officially there is a difference. If you know IPA: כ is pronounced /k/ or /x/ and ח is pronounced /ħ/. Essentially, כ is pronounced either as an English "k" or as "ch" in the Scottish "loch", and ח is pronounced like "ch", farther down in the throat.
The food (which we know of) is hot - we already know about the food (possibly we can see it on the table). The fact that it is hot is news to us. Thr hot food - we already know that the food we can see is hot, and now we are referring to it, possibly in contrast to the cold food. In Hebrew, the first example is האוכל חם - only the noun is informed using the ה'. The second example is האוכל החם - both the noun and the adjective are informed, each with its own ה'.
The leading ה is not a subject marker, it is the definite article ("the"), and goes on a definite object as well as on a definite subject. As you've seen in Nir's example, the definite article also goes on an adjective modifying a definite noun.
And yes, "אוכל חם" means hot food.