Went to relatives house once, and the toilet werent flushed. if there are sperm in a public restroom, and the toilet water splashes on a womens private part, will that be enough to make someone pregnant?

Pregnancy is not possible in above circumstances. Hand hygiene rules still apply and should be followed consistently.

No. Sperms have to enter inside the vagina to do that

Sperm from semen is rendered inactive when in water, or on surfaces and outside of the vagina in 3-5 minutes. Sperm has to enter the vagina in fresh condition during ejaculation. Safe sex leads to no pregnancy and worries.