Yes, both versions (with and without です) are commonly used. You can use just もちろん with your boss or someone important, and it probably won't come across as rude (of course it depends on the context and your tone), but adding です makes it more polite. So if you're not sure if you can get away with it, it's better to play it safe and add です.
Hmm, もちろんです is used to kind of emphasize the obviousness of your response, a la "did you even need to ask?", and so you could say that it's less polite. But I think your tone can make it sound good-natured and equally as acceptable as そうです in many situations.
So, I don't think you can really compare it to そうです in terms of formality. もちろんです sounds more like a response, as opposed to a confirmation or agreement like そうです.
I have already explained it on this discussion page a number of times. Please read the comments before posting.
Copied from an earlier comment: There are cases, like this sentence, when it's essentially added just to be polite, but in most cases, it also serves a specific grammatical role (the copula).
Yes, if you used です at the end of every sentence, you would sound weird (and grammatically incorrect). But, that doesn't mean it isn't important. There are cases, like this sentence, when it's essentially added just to be polite, but in most cases, it also serves a specific grammatical role (the copula).
Becasue Japanese loves to rely on context, but Duo doesn't give us any.
If you break down ええ、もちろんです, ええ means "yes" (spoken form) and もちろんです means "of course", so in what context could it mean "Yes, I am fine"?
If someone asks you お元気【げんき】ですか, they are asking "how are you?", but literally, the question is "are you healthy/in good spirits?". So, when you answer ええ、もちろんです, you are literally saying "yes, of course (I am)", but Duo chose to teach it to you as "yes, I am fine" which works in the right context.
Following stroke order is highly recommended, especially when you're learning new characters, but most of the time, people won't notice if you get it a bit wrong :) especially if it ends up looking correct.
As for Japanese handwriting, having worked in Japanese schools, let me tell you it runs the whole gamut, just like English handwriting. Some of my middle school students had beautiful, flowing, evenly spaced writing, while others had barely legible chicken scratch - some of the teachers as well...
Here's a post on Reddit that covers it really well: https://www.reddit.com/r/japan/comments/1hcf6j/does_japanese_have_differant_handwriting_styles/cat26of
Why wasn't '勿論です’ accepted? Also, why is there no option to report 'my answer should be accepted' with audio transcription exercises? It seems there is a wide variety of situations, especially with Japanese, where the same phrase can be written correctly in multiple ways and only one way is accepted by duolingo