well, we always suggest using condoms WITH birth control since that significantly reduce failure. If you're already missing pills, you're not going to get maximum protection from your birth control. so in short, regardless of your period, you need to be using both condoms and birth control.
Just to make more clear the answers to your questions:
1) One late pill, taken less than 24 hours after it should have been, will reduce your effectiveness, but does not present a LARGE pregnancy risk. As is perhaps obvious, the pill alone, regardless, doesn't offer STI protection, so you still have those risks in full.
2) You don't actually have a period if you're on the combination pill, you have a withdrawal bleed. Any type of sex during that time poses no additional health risks save that, again, if you're having partnered sex without latex barriers, STI risks are increased then.
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