It means that he is crazy.

I agree with Derrick. If it's a business situation then you should use both names but don't stress either one. If it's a purely social situation then I only introduce people by their christian (first) name.

«It seems to me you're tired» means the same as your earlier examples. «I seem you're tired» is incorrect though.

I can't remember how old I was when I started watching but Jon Pertwee was the Doctor back then :) David Tennant is great but Tom Baker was my favourite.

We are hoping for an improvement in the weather next week.

Both are correct but there is a subtle difference: "English is your hobby, isn't it?" implies that you already know the answer and are looking for confirmation, while "English is your hobby, is it?" is more of a direct question.

"Until then" suggests that you have made plans for something to happen in the future - meeting or speaking. With "Goodbye" it is a little more flexible (and formal). It doesn't speak about the future so can be used whether you are going to see/speak again or not.

I wouldn't say it is common but it's not so unusual. It is only likely to be used between friends and I believe that it's more common in the UK than in the USA.