Can you become pregnant hveing sex 1 day before fertile days?

Yes. Sperms can survive for 48-72 hours and pregnancy can happen by having sex 1-2 days before fertile days.
Yes. While human bodies are amazing, they aren't always predictable. It's difficult to measure exactly when your most fertile days are, so if you aren't planning on becoming pregnant, use things like barrier methods (condoms) or hormonal birth control. Rhythm methods or the "pull out" method are unpredictable and not standardly recommended for birth control.