Question: Does the major you declare on an application for admission affect your acceptance? Are there fewer openings for engineering majors and does that mean you need higher test scores if you apply to the engineering school?
Sometimes declaring a major can have an effect on application success. For example, if you put "pre-med" on your Johns Hopkins application, you're more than likely going to jump into a more competitive pool than you would if you put "liberal arts." That's because Hopkins is known primarily for its pre-med program (among other area, to be sure) and attracts lots of applicants for that major.
Same thing for engineering. At most universities, the engineering school requires an extra level of selectivity. This extra level usually requires, as you note, more competitive test scores, stronger grades in science and math, and special emphasis in these area on recommendations.
Usually, you'll have to make some kind of direct statement about your desire to gain entrance to the engineering school on your application, whereas in the case of a pre-med-seeking applicant, s/he might indicate a less-competitive area and then change majors once admitted. There can be some strategies involved, so it does pay to do research before you begin to structure your application.