"Because it is interesting, I study Japanese."
Kara here is used to tie together reason between action and main theme. Omoshiroi kara - due to [the theme] being interesting. Nihongo wo benkyoushimasu - studying Japanese.
It usually helps to read the sentence backwards - it would be something like "I am studying Japanese because of its interestingness".
No, you cannot. You can say 'omoshiroi desu (the sibject you are talking about is interesting). But by using 'desu', you are completing the sentence. When you use から (explaining the cause), you need to continue the sentemce.
For example, びょうきだから、がっこうをやすみます。Because I am sick, I won't/don't go to school.
When we explain the cause, you can also use なので、or だから as well. I hope it is not too much...
The だ in だから that you're thinking about is in fact the informal form of ですanyway. It's most common to use polite forms in sentence endings and informal forms everywhere else, but you can in fact use formal everywhere in some cases like in business correspondence and news broadcasting, etc.
Well, there are many instances where you cannot substituteです with だ, such as using these phrases: verbと思います ( I think that...) or verbといいですね (I hope that you...). In these instances, the verb before the と MUST be in the plain form (e.g. たべる、 たべない、たべた、たべなかった）; therefore, using です in these instances makes the sentence incorrect. In response to Juanluis42's answer, I agree with what he/she is saying to an extent: you cannot use だ and です interchangeably, like in my previous examples. But regarding your specific question, ですから is more polite than だから。だから/ですから (however) and だけど/ですけど (but) are examples where です and だ can be interchanged, with です being the more polite variant. But all in all, I'm not a native Japanese speaker, and this debate can become very nuanced when diving deep into the topic. I hope this helps! Check out this website for a more in-depth look at だ vs です! :) https://www.tofugu.com/japanese/da-vs-desu-in-real-life/
How is that? だ is not an informal form of です. だ is for declare what you say and some sentence connections, and can be used here. です is only for politeness, and cannot be used here. You can read more about it here: http://www.guidetojapanese.org/learn/grammar/polite#_is_NOT_the_same_as