This topic is way too broad. You cannot simply "explain" someones mind. Example:Explain your mind to me.
A: Study in Scarlet.
Actually, yes! He is engaged to marry the housemaid of Charles Augustus Milverton although, in his mind, there is nothing romantic about it.
No. Just an incredibly precise and trained mind.
Yes he did. In almost all of them. The one's that come to mind are: "The Adventures of Sherlock Holmes" "The Hound of the Baskervilles" "The Woman in Green"
The cast of A Slight Trick of the Mind - 2014 includes: Ian McKellen as Sherlock Holmes
Keep in mind Sherlock Holmes is a fictional character who "lived" at 221B Baker Street (not even a real address), but it would have been about 13 kilometres (8 miles) west of Whitechapel.
There's two possibilities: 1. He's a time lord. This could explain how several different actors have portrayed him and they all have a slightly different demeanor. 2. Sherlock Holmes never traveled in time. Where did you even get that idea? Honestly what is going on in your mind? Are you getting mixed up because BBC's Sherlock takes place in modern times, or that the less interesting CBS show Elementary did the same things Sherlock did but made much more bland? Did they not make it perfectly clear that those shows do not depict the real Sherlock Holmes? Both of them are modern adaptations of the classic novels, (But BBC's Sherlock is much more faithful.)
Boredom, he needed to keep his mind working on something really complicated or he was bored all the time.
He places Monsieur Bertillon above Holmes as having a more precisely scientific mind.
Sherlock Holmes enjoys fencing, talented at fencing but most of all, he loves the violin as well as music itself and to test out new chemical experiments. According to him, his mind starves for things to think and to do.
According to Sherlock, it is his brother, Mycroft. He never liked to leave his club or office and certainly didn't want to go out investigating. Sherlock would sometimes consult with him and Mycroft sent work his way.
He could indeed be expressive. Remember him grinning more and more as that guy called him a busy-body among other things? However, if you mean "made into a cartoon", then, certainly. Check out Sherlock Holmes cartoons, Sherlock Hound (anime), Sherlock in the 22nd century and others. There are also animated characters very much like him. Jimmy Kudo/Conan Edogawa, L of Death Note and The Great Mouse Detective (Disney) based on the children's book series Basil of Baker Street come to mind.