So I’m going to be submitting my college apps in a couple of days, but when I look on common app it states that my teachers have not yet started their letters of rec yet. Can I submit the application without it being complete? And can my teachers still complete the letter of rec after the application deadline for a school?
Yes – this is commonplace. Colleges WANT to admit you. If the LORs are particularly late, they’ll contact you or the school. You’re fine
Yes, that deadline is for your application. If your recs or test scores arrive a few days late, it just means that your file is incomplete and it will delay the review. If schools rejected out of hand every application that wasn’t complete on the day of the deadline, their selectivity ratios would drop like a rock (and they’d lose a lot of great applicants). They want you to apply - they will wait for your other materials. (And even if your application is a day or so late, they will probably still consider it - but it suggests that you are either very disorganized or not very interested in the school.)