Yes, Peter, from the way you describe it, it sounds as though your chair is upset, and for good reason. You've gotten a lot of excellent advice here, so I won't repeat all that. Instead, I'll try to answer your questions and help you to see where you went wrong. You didn't say where you are, so note that my comments below apply to the United States. Norms might be different elsewhere.
My questions are
1: should I ask help from the dean without notifying him?
Absolutely not. That's called "doing an end-run" or "going over the head of" your department chair, and both are frowned upon, especially by the person you've done the end-run around or whose head you've gone over. It's very bad form to do this, except under the most dire of circumstances.
2: can he forward my email to others?
Absolutely. So can anyone else. Never put into an email something you want kept confidential, unless you completely trust the recipient not to share it with anyone--and even then, think twice.
3: can he ask my marriage status?
When? He is not supposed to ask before making a job offer (although many people do, often as part of the casual conversation that accompanies a meal or other "social" time during the interview process). After you're hired, sure, he can ask. But whenever the question arises, you're under no obligation to answer it, if you don't want to.
4: if you were in this situation, what will you do?
I would be very, very nice to the people who were trying to help me--and I'd also be encouraging SO to send out lots and lots of application letters, etc. (i.e., to look for work independently of any efforts the university folks made on SO's behalf).
I welcome any comments and suggestions about this issue.
I'm very sorry that you're having the two-body problem. I've got a two-body problem, too (I'm the "extra" body), so I truly do understand your plight. But look at what you did, from your department chair's point of view:
1) After learning that you had an SO who needs a job, he contacted the top administrators at your school and solicited their help in finding work for your SO. Truthfully, there's probably not much more that he can do. He can't force anyone to hire your SO, assuming there are even any appropriate job vacancies. And he certainly can't force anyone to create a job where none exists. All he really can do is ask and, maybe (depending on a lot of things), try to persuade.
2) After learning that none of your deans could help you, you met with your own dean to explore the problem further. If you did not tell your department chair about this meeting, he likely thinks that you don't trust him or you think he's incompetent. Either way, it was inappropriate to leave him uninformed (a) because he was trying to help, and (b) because he is in the chain of command between you and the dean, and it's bad form to skip links in the chain of command--especially when you're new.
3) After all that, you then sent an email to the department chair and, without acknowledging the efforts he or anyone else has made on your behalf (successful or not, people have tried to help), you complain that everyone is just sitting around talking about your problem instead of solving it. You seem completely unaware that it is
your responsibility to solve the problem, and these people are simply doing what they can to help, however much or little that may be. They are not obligated to solve your problem.
4) If you had told the chair about your two-body problem in your application letter, you might not have gotten the offer, it's true. I am certainly not saying you should have mentioned it in your letter (you did the right thing by not mentioning it), even if that's what your chair is saying. But you do have to understand his frustration: He went through a job search and he hired you thinking that he had successfully filled the vacancy in the department. Now he's finding out that he may have to go through the whole process again, if you and your SO decide to leave. That's not your problem (just as your SO's need for a job is not the chair's problem), but it's probably the reason he said you should have told him about the two-body problem in your application letter. He is probably thinking that he's got problems either way: If you leave, he has to run a new search. If you stay, he has a whiner on his hands, and worse, a whiner who runs to the dean behind his back.
As I said, I do understand your frusration. But it sounds like you also need to learn a lot more about the academic culture, in general and especially at your school, and then follow the norms. And you need to recognize which problems are yours to solve. Good luck to you.