"Nice to meet you, I am Maria."
Kanji helps with reading. In Japanese, there are no spaces between words. Kanji helps with breaking down large blocks of text into chunks of words, and makes reading faster. It's easier to see and recognize a single character than reading individual syllables (with kana) or letters (Roman alphabet). "わたしはたなかといいます" is longer and harder to read and break down than "私は田中と言います" because the individual kanji helps you recognize the different words and the hiragana particles act as "spaces" that show where one part of the sentence ends and the other begins (while also pulling double duty and showing how the parts of the sentence relate to each other). It also helps with homophones. That way you can easily differentiate 神 (god), 髪 (hair), 紙 (paper), and 加味 (seasoning), which are all pronouncing かみ (kami). Sure, there's also context, but it still helps with making reading faster (like the different there, their, they're) and it stops you from adding hair to your food.
Your case does not exist as it is not reasonable that you would need to tell the person you are talking to what his/her name is. You can make a question like this by ending with Desu Ka, but it would still be very very rude to mention a person you meet for the first time by first name and without San or Sama.
Not really. In this context omission of subject is far more usual than not.
If I am to pick faults it is about using first name and Desu, which makes the sentence only useful in certain scenario, e.g. between young people in a relatively casual situation. This somehow fits the level of this course.
Why does it tell us that it is pronounced as "kito but then tells us that it is written like" じん ?
The issue with よろしく is that there is no set meaning. It is used in various circumstances with various English translations. It is basically said to foster goodwill going forward and/or to entreat someone to treat you favorably. It can be 'I look forward to working with you', or 'I hope that we get on well', or many other paraphrased translations, but nothing too specific. (copied from another thread)