I was wondering, do cores taught by different profs for in the same course generally move at the same pace? Also, is the material taught in the same order? I'm asking because I'm worried I might miss a lecture and have to attend a different one. Or, if I want to study with a friend that's in another core I'm worried one of us might be behind or ahead of the other in terms of material taught.

Yeah they teach the same material in the same order, or at least they did in all my classes for science! And you'll only ever be one day behind/ahead of a friend in a different core, let's say your class is on Tuesday you'll have the lecture earlier then someone on Wednesday but it's not much of a difference and you can go to other cores and get the same information but for iclickers you can only answer iclicker questions in your own core! Usually for midterms all material will need to be covered by all cores by a certain time so studying with a friend should be fine!

Generally yes. Even if one section is behind/ahead they try to keep it in sync so that all sections have the exact same knowledge before an assignment or a midterm.

Just keep tabs through people who are in other cores before you decide to go to them. Even though like they said it's usually only a 1-lecture difference tops, it would suck to plan to go to a lecture that's already ahead of you.

It depends largely on the prof; I had the same physics prof both terms and both terms he finished the material 1 or 2 days ahead of schedule (and the other cores).