Yes, you will need to have SAT scores sent directly if the college doesn’t allow self-reporting. No, you will not be rejected if the scores aren’t in by the deadline (as long as the rest of your application is complete), but you should arrange to send them ASAP (especially to colleges considering students for competitive programs on a rolling basis). Colleges are aware of the timeline for the December SATs, so they know about when to expect them, and the delay will be overlooked, but only to a certain point. In most cases your application will not be reviewed until it is complete, so it is to your advantage to get them in as quickly as possible.
Check the colleges websites for IELTS, or else email admissions. It is probably similar to the SATs, meaning have them sent ASAP. You don’t want multiple test scores arriving after the deadline. While colleges are understanding about the December test dates, getting multiple scores in after the deadline might look like poor planning.