1. To be honest, there are security risks in this part of the world, with current threats and new ones emerging periodically, you have to accept that if you come here. But, the US Embassy will give you tips about 'how to be safe' (really its mostly common sense) as well as contacts for what to do in case of an emergency situation. In general I would say that westerners are reasonably safe here in Qatar.
2. Don't know what police actions you are talking about - can you give more information?
3. Your employer will control YOUR visa, but not your wife's. So, to leave the country you require permission from your employer as they will have to approve your travel in order for you to get an exit visa to leave the country. Your wife however will be here on a family visa sponsored by yourself - as such she is free to leave Qatar anytime she likes, without an exit visa, although you will probably get a text to say that she is going, and if you have children, it is best to have a letter from you to say that she can take them from the country. She needs a re-entry visa to come back.
4. How women are treated - that depends on many things, including how well your wife copes with any potential attention. It is like anywhere, different people treat you in different ways - some will be very friendly and happy to speak to you - others will appear as aloof, but in fact are dealing with you in a respectful islamic manner (won't touch, speak, look at you). Others, mostly young men (late teens/early 20s) and/or workers from Asian/subcontinent/Africa who are single and have been here awhile will leer and may speak to tell you how beautiful you are or ask if you are married or for your phone number. Male workers in government departments or companies etc are (in my experience) always helpful and in fact it is often to your advantage here to play the 'helpless/dumb woman' as it opens doors to the most efficient way to get things done (my husband hates that it takes me 1hr to get something done that takes him half a day! A friend recently got her 6000QR traffic fine reduced to 1500QR by doing this). You will also come across those men that will consider you to be 'beneath' them, but in all honesty that is often because you are an expat, not because you are a woman, they treat men in that way too.
If she has any specific questions then feel free to send me a message.