1) Found on train in Japan:
この席を必要をされているお客様がいます。
So this is about those seats being reserved for passengers with special needs. But how does 必要がされている work as a grammatic structure? And to me it seems like がいます would refer to the guests/passengers, but surely they mean the seats. Then how does the を work? I'm truly lost at this one...
います will never be referring to 席, as います refers to animate things, such as people.
を必要されている is the honorary passive of を必要している. Often in Japanese people use the passive to be polite. For example:
先生、どこに行きますか? -> 先生、どちらに行かれますか? -> 先生、どちらにいらっしゃいますか?
All of these translate to "Teacher, where are you going?" (do NOT translate 行かれます as the passive, it's just showing respect not a grammatical function). And as you can see, the honorary passive is between just the normal -masu form and the more formal いらっしゃいます, making it nice for sounding polite but not too stiff.
b)ありがとう。よくなりました。あなたにも心配させってしまって、ごめんなさい。
Is a) trying to politely express his concern for b) overworking himself? I have tried to translate this to English, but I'm not really sure how to express the first sentence.
*あなたにも心配
させてしまって、ごめんなさい
"Sorry for worrying you" or "Sorry for making you worry"
させる is the causative of する, so it would mean "to make" or "to let"
心配する to worry -> 心配させる to make (someone) worry
By the way, for 妻に出ていかれてしまいました, this is often called 迷惑受身 or the "suffering passive"
It's a passive construction to show something negative is happening.
For example, こよなく可愛がっていた犬に死なれた
How Angel Valis translated the sentence with 妻 is fine, but if you tried to translate 犬に死なれた in the same way as a passive sentence it would come out sounding very funny (ie, please do not translate it as "I was died on by my dog"). Instead it means something more along the lines of "My dog up and died on me"
It's common to hear 雨に降られた as well, which is also suffering passive