Am I allowed to work? I did not manage to get scholarship and working is very important to me.
Basically, no. There is very little chance that you will be able to find a job, even less so one on which you could support yourself, your wife and your child in Poznan. If you do not have enough cash to pay your way through your whole study period, forget about coming. Of course, chances are even lower that your wife will find work.
Sorry, but it does not appear that you will be able to study in Poland, especially if you are expecting to bring your wife and child along. Without a 100% scholarship that covers your tuition and apartment, there is nothing you or anyone can do.
Engineering management
Engineering management courses are generally not very useful for finding high paying jobs. Your time would be better spent beefing up your engineering qualifications than taking a whole bunch of time consuming and useless management courses. Try getting a degree in petroleum engineering, geological engineering or biomedical engineering at a good school in Egypt.
Any information about the PR? do my years in the university will be considered as part from the 5 years needed to get the PR?
As I said, studying in Poland is not a viable option for you. There is no advantage for you in coming to Poland to study. If you are thinking of Poland as an easy back door to the EU, think otherwise. That would be a foolish mistake, and you will waste a lot of time and money.
Get a more useful and salable engineering degree in the fields I mentioned from a good school in Egypt or other country in the region, and you will have little trouble finding high paid jobs anywhere you want. Those specialties are in high demand and demand will increase throughout your lifetime.