Additionally, I believe in Italian, there's no distinction between the continuous present and the simple present like we have in English--usually.
"I am eating" and "I eat" would both be "Io mangio".
There still is a continuous present, however, but it's only used to emphasize the ongoing nature of an action. It uses the verb "stare".
So, if you need to specifically say "I am eating" it would be "Io sto mangiando".
Completely. The first accent you wrote is called accento grave, the second one is accento acuto. The root vowel is the same but it changes the sound. So it is used to make a distinction about the sound of the word and in some cases the meaning of the word. Every Italian word has an accent, called accento tonico. It gives you an hint abou the syllable to be stressed. For the written text and for the majority of Italian words it is not mandatory to express the accento tonico. However for some words is important because according to sound that word changes the meaning completely. The classical example: pèsca, it means the peach (the fruit). pésca, it means the fishing.
I entered "caffé caffè" into Google Translate and Reverso.Net, then played the computer-generated sounding of the words featured at both sites. I heard a very distinct difference in the way the é and the è are pronounced. The best way I can put it is that the è is "voiced" and the é is "unvoiced".
For the voiced è, you form your mouth to say "eh" (like the "e" in "yes") and then, keeping the tongue in place, say "ay" (as in English "hay"), letting your tongue drop back a little. You want an "eh" sound which is heavily tinged with "ay".
For the é, you put your mouth in the "eh" position, but say "ih" (as in "bit"), letting your tongue move forward towards the teeth. You want an "eh" sound which is heavily tinged with "ih".
The point here is that, when the tongue is further back in the mouth, you get a sound that comes more from your throat (is "voiced"), while, when the tongue is closer to the teeth, you get a sound which comes from the front of your mouth and doesn't involve the throat (doesn't involve the "voice").
I don't really know how important this distinction is in every day Italian. I'm studying Russian, also, and voicing makes a big difference there, because it changes the meaning of words - lots of them.
Just like you said, it is usually always used in the Italian language, as opposed to English. In fact, if you used the definite article ALL the time, you would be correct. There are some instances where it would be better if you omitted it, however you wouldn't be incorrect if you didn't. An example where it would normally (and preferably) be omitted is when creating a shopping list. You would not use the article in front of the noun. However, if you do, it would still be correct.
Now on the other hand, there are times where you MUST use the article, and you would be incorrect if you do not.
So when in doubt; USE the definite article in front of the noun.
So why is "Lei beve il caffè" wrong? I understand that "Lei beve caffè" is a better translation for the original sentence, because in english it doesn't have an article, but after reading what you wrote here, it seems that it is Duolingo that is wrong on this one. Don't get me wrong, I love the software, but I am Brazilian and started using to learn english, and I must say, sometimes it is wrong (cases in italian may be similar with portuguese ones. Nuances that english doesn't have).