As mentioned earlier, mechanical engineering is a competitive program to get into. Make sure you don't drop any courses in first year eng, because you are just making it harder for yourself to get into a competitive program. Second year engineering admission is based on the number of points that you have in first year.
lets say that you need a 7.0 in first year to get into mechanical, that means you have to have a 7 over 37 units (full course load). I'll demonstrate using an example:
1st student:
7.0 x 37 units (full course, meaning that student didn't drop or fail anything) = 259 points
2nd student:
7.0 x 34 units (not a full course due to dropping/failing 1 course) = 238 points
Therefore, if the cut-off for mechanical that year was a 7 (259 points), the first student would get in, but the second would not (even though they have the same average !!). In order for the second student to get into mechanical he/she needs: 7.5 x 34 = 238 points... that's why if you drop/fail anything in first year engineering you have to make sure that you work really hard to get into a competitive program!
To answer your first question, yes, everyone in first year engineering takes the same courses, except for the electives.
This website is helpful:
http://www.eng.mcmaster.ca/eng1/requirements.html
Just a quick note, in the website above they say that "The completion of your complementary studies electives (6 units) are not required for admission into Engineering II", that's true because you can take your electives anytime, not just in first year....but when they calculate your average to get into second year (in particular, a competitive program) they do it based on a full course load (37 units). That's why its better to have a full course load in first year eng.
Good luck !