alsalamu alikom wa rahmatullahi wa barakatoh
first of all I recommed to repost your question not on the general fourm but on the electrical fourm uder this link to get the most profissional answers.
I will try to ansewer some of these questions as per my general engineering knowledge.
As a general common features for all engineering devisions, there are 5 applications fields for engineers work
Rsearch (which is concentrated on the engineering scince research in order to discover, improve and modify the engineering as a science and technology). And this commonly found on the universties, research councels and Engineering associations
R & D research and developement (this is a field of applications which concentrates on studing the product analysis and the excution process analysis in order to improve the product quality and increase the productivity of the plant as well as to reduce the production cost). this field is almost found on the standard products companies
Design (this is a field of application which concentrates on the prduct design. Design word is a general word which can be classified into many applications shuch as the conecptual design, the prduct itself design based on the selected concept and the cosmotic designs and modifications in order to improve the product
Production (this is the filed of application at which the real excution of the produc will be carried out. this field can be displetted into two divisions. the production devision and the QC/QA devision). this field is exist on all production companies
Maintenance (this is the field of application which concentrates on either to keep the production plant itself working smoothly without undesirable shutdown, or to introduce the maintenance services for thier products users during thier prduct service life). and I think it is clear which companies needs these type of engineerig field
Planing and follwoing up, And Business Developement (this field of application is not easy to talk about it but let me say it is the field which concentrates on how to manage the resorces in order to get the best facility performance with the lowest costs, and also the futre forecast, and you can say how to icrease the plant profits and market shareing). this department is sould be in all facilities.
If you read what I wrote I think it will be something clear that your questions are almost general questions which are very loose and not acurate enough. i.e the limitations are less than the degrees of freedoms which gives infinite number of solutions. but even if I can say that, the most common field on the electrical engineering is the electrical contarcting such as the electrical supply and feed to the cities as well as the electrical network design and constrcution inside the facilities like ABB company on the 10th on Ramadan.
excuse me for any typing mistakes since I don't have enough time for rechecking the text.