How to deal with Unprofessional and Arrogant Boss

 I would not be concerned with them making fun of you. That is their behaviour and is not a reflection of you. Sure you could tone it down to fit in better but is changing like that being authentic to yourself. You have decided to be a little more professional than the others there is no shame in that as long as it is within reason. It's not like you are wearing expensive suits on an oil rig. 
While it may be frustrating that they are making fun of you and then tuning to you for the difficult tasks you should be honoured. They are turning to you because they know you can get the job done. Remember it is the results that count. 
s

At one point in my career, I was in a similar situation.  Dealing with the situation required setting long- and short-term personal goals.
My long-term goal was to obtain a promotion in a my field within my (or another) company.  To do that, I needed to expand my range of experiance within my field.  I had been too narrowly focused in one area of specialization, and when I looked for promotion I realized that this issue would hinder my progress.  My short-term goal was to stay in my unpleasant situation until I had demonstrated ability to perform in multiple areas of expertise.
Having personal goals, outside of whatever drama is created by one's boss or others within a department, helped keep me on track and have a more positive attitude with people I worked with outside my department.  When I finally was ready for a new job, I found that those contacts I had made in other parts of the organization helped me get the promotion I was looking for.  It turned out that my boss's poor behavior was known and not appreciated by people in other departments.  My willingness to help other people get needed project deliverables from my difficult boss won me quite a few fans, which I didn't realize until I was in my new position.
Since you indicate the lack of professionalism exists at the highest level of your organization (CEO), I would recommend concentrating on what you need to accomplish to find a new organization to work in.  You cannot change your boss's behavior, but you can change your situation.  Your boss's behavior reflects badly on her, not on you.  It does not seem like your boss is truly interested in firing you (I find what people do, rather than what they say, is a more accurate way to predict future behavior), but you should not waste more time in this organization than is needed to support your career and financial goals and responsibilities.

At one point in my career, I was in a similar situation.  Dealing with the situation required setting long- and short-term personal goals.
My long-term goal was to obtain a promotion in a my field within my (or another) company.  To do that, I needed to expand my range of experiance within my field.  I had been too narrowly focused in one area of specialization, and when I looked for promotion I realized that this issue would hinder my progress.  My short-term goal was to stay in my unpleasant situation until I had demonstrated ability to perform in multiple areas of expertise.
Having personal goals, outside of whatever drama is created by one's boss or others within a department, helped keep me on track and have a more positive attitude with people I worked with outside my department.  When I finally was ready for a new job, I found that those contacts I had made in other parts of the organization helped me get the promotion I was looking for.  It turned out that my boss's poor behavior was known and not appreciated by people in other departments.  My willingness to help other people get needed project deliverables from my difficult boss won me quite a few fans, which I didn't realize until I was in my new position.
Since you indicate the lack of professionalism exists at the highest level of your organization (CEO), I would recommend concentrating on what you need to accomplish to find a new organization to work in.  You cannot change your boss's behavior, but you can change your situation.  Your boss's behavior reflects badly on her, not on you.  It does not seem like your boss is truly interested in firing you (I find what people do, rather than what they say, is a more accurate way to predict future behavior), but you should not waste more time in this organization than is needed to support your career and financial goals and responsibilities.

Wow, you really sound unhappy, but I don't think there is much you can do.  I was at a manager-tools conference and had a chance, with one of my colleagues, to speak with with manager-tools presenter over drinks.  We spoke a little about the challenges we were facing about our boss.  In the end, she said there was nothing we could do since we couldn't manage up.  It was frustrating to hear, but in the end, it was true.
What Ive learned in life is that once someone treats you a certain way, they think they can always treat you that way - on the job you don't have to be loved, just respected.  You could try to talk to him in private, but why bother.  I would say just accept it, let it go, and look for a new job- it just isnt working for you.

 I think there is actually quite a bit you can do.  You can not change your boss behaviour but you can change the way you perceive his behaviour.  The way to get around it is think to yourself what the consequence of his comments are.  In fact he is the one that looks ridiculous on his spiral notebooks and holiday in pens!  Of course you will not make fun of him out load but you can make fun of him within yourself.  People laugh out of their jokes out of fear, they don't think they are funny!  "How you feel is your fault."  It is your choice to let it affect you or not.  Of course this is easier said than done, but start by faking it and soon you will feel it is funny (how he comes out in a spiral notebook!).
The other thing you can do that will help is concentrate on behaviors and not labels.  You have put three labels on your boss: unprofessional, arrogant and stupid (doesn't know anything about the job).  It maybe right, I don't have enough information to say he is not, but you have also not given enough information to confirm he is.  And even if he is, nobody is unprofessional, arrogant and stupid all the time.  You have to understand that these labels come from your perception of it.  You probably look as arrogant to him with all your engineering and GTD knowledge (something he doesn't have and probably feels threaten by not having it!). (I am an engineer myself, so don't take it personally.  I have since learn to identify, not necessarily avoid, my own arrogant behaviors!).  Also while I believe more technical knowledge at the higher positions in the companies would do them great (bias opinion as I am an engineer myself), I have seen lots of prejudice from engineers on failing to recognize people's capabilities blinded by the fact they had little technical knowledge!  Well, they bring something else to the table that most engineers fail to bring or else they would not be there.
So suggestion to you is to take the opportunity to identify what it is that they bring, that is different from what you bring and learn it too.  And accept that your role is to bring in the technical aspects that they don't know.  I know it is very hard to discuss technical aspects with somebody that has no knowledge, but it makes things harder if you fight them.  You must show them that you value their input, and they will start seeing you more on their side rather than against.
With regards to threatening you your job is on the line, that is definitely not nice.   I think the internal network recommendation given here is an excellent recommendation.  Other than that if you believe the threat is not real don't worry about it.  You already figure out they are just trying to bring fear.  If you think the threat is real, actually either way, get your resume ready.
happy new year!  I hope things improve!
 
nara