There is a full core, lab, and tutorial that would solve the conflicts in my timetable, is there someone I can email to get into those sections?

Keep checking Solar. A lot of people will be changing their timetables till the first week of September.

Yeah keep checking definitely. But if you're really worried try emailing the department head or if it's an eng course try Sally Williams perhaps? There's still plenty of time. If its an elective there's no guarantees, but if its a required course sometimes things can be moved around.

Okay will do
But so if it's a Phys 1E03 core I should email the department head of physics?

Just attend those core/lab/tutorials for the first few days of class, since thats the only way you will be able to have a conflict free schedule.
and keep checking - i believe the last day to drop/add classes without financial penalty is sept 14 (i think?) so people will be changing stuff alot before then. if its close to that date and youre still not officially in those classes according to solar, email someone and explain, they should let you in

EDIT: I cant remember who you email, sometime you email the prof, and they are able to open a seat for you. I think you only email the department when you are trying to get into a class that you dont have pre reqs for or something.