"I am busy on Tuesday."
I use an app called Obenkyo, which should be completely free, and I absolutely adore it. It has a lot of features, but I have so far only used it for kanji. It lets you choose which kanji you want to study, then you can either choose the meaning/reasons of the kanji (multi-choice), choose the kanji from the meanings/reading, or my personal favorite, you can draw the kanji, and it checks shape and stroke order. Check it out: https://play.google.com/store/apps/details?id=com.Obenkyo
Duolingo has another website where you can study language terms. Here's a link to some of the kanji. https://tinycards.duolingo.com/decks/0baf9a79-2bc9-41b0-b8a8-6439c9f6f5a4
It should be に and not は because the sentence is I am busy on Tuesday. The whole sentence should then be 私は火曜日に忙しいです。私は is omitted as it is not necessary, and you are left with the rest. Putting は after Tuesday is then mistake as you can't have two topics in a sentence.
If I'm wrong someone please explain me why.
You are wrong, I'm afraid. The topic here is Tuesday, not I. Both "ni" and "wa" are correct, just a nuance is different. When we use "ni", it only means "I'm busy on Tuesday" while using "wa" makes the translation something along the lines of "As for Tuesday, I'm busy". It all comes down to the same meaning of course but the emphasis is slightly different.
I also use kanji senpai, you have to pay for audio, like 600 words for 2.99. Each lesson is that way and they are grouped by JLPT level so you can get just the ones you are ready for.
I also use kanji tree, which is free, but has no audio.
Both of those apps have kanji with different readings and drawing practice.
Why does Duo only accept ”火よう日" （kanji\hiragana\kanji) but not "火曜日" (all kanji) or "かようび" (all hiragana)? My computer requires SO MUCH effort to get it to do the weird kanji/hiragana combo (I have to type the whole word kanji, delete the last characters, type the middle hiragana, then type the whole word in kanji again and delete the first characters.) In Japan, I usually just see it in the full regular kanji. Why is that not accepted?
Because this course is still in beta so it doesn't have all the correct translations accepted yet. Since the middle kanji is very difficult and hasn't been introduced yet, its "preferred" translation at this stage is this weird combination. Report this missing "correct solution" and I'm sure it will soon be added to the list of acceptable alternatives.
I have a question. If I for example wanted to use ''Watashi'' in this sentence, would it be correct if I said ''Watashi wa kayoubi isogashii desu'' or would I have to add the particle ''ni'' in that case - ''Watashi wa kayoubi NI isogashii desu''. The sentence ''Kayoubi wa isogashii desu'' talks about ''kayoubi'' since that is the obvious subject of the sentence, hence the particle ''wa'', and because of the context we can assume that the sentence is actually about ''me'', but what if I want to make it clear who is the sentence about, and use either personal names or pronouns, would the sentence be any different that way?