Situation two: If there are not two kosher witnesses, and the act was done on purpose there is nothing one can do but repent. Repentance means that one accepts upon himself not to repeat the act. This by definition brings Divine forgiveness.
Situation three: If the sin was done by accident [for example a man thought it was his wife in bed with him] then he must bring a sin offering. This can't be brought anywhere except in the Temple in Jerusalem. In fact, bringing a offering anywhere else is a sin on the same level as homosexuality. This is explicit in the Torah (Old Testament) itself. That means that at the time there was a movable Tabernacle, one could only bring offerings there. And to bring one elsewhere is a sin of "cutting off" (which is called karet כרת in Hebrew). Once the Temple was in Jerusalem, it can't be erected else as Nathan the prophet said to King David.
So nowadays we (Jews and Gentiles) can't bring a sin offering anywhere. However repentance is always open to every person and always helps. (Repentance is accepting on oneself not to repeat the sin and confession before God and feeling guilty about the sin.)
No matter what where the circumstance repentance always brings some measure of forgiveness.
[If not for the words of Nathan the prophet to King David, then we would be able to build another Temple anywhere in the world. The problem nowadays is that Nathan said the Temple Mount would be the only place God would rest his presence from then on. So we are kind of stuck.]
Appendix: Repentance is simply accepting on oneself not to do the sin that he did. How do we know this? From the law that if a person does kidushin [marries a woman] on condition that he is a perfect saint even if he is a perfect criminal she is considered married because of a doubt: he might have thought not to repeat his sins ever again at the time he made the marriage. So we learn that if he in fact did think to never repeat his sins he is in fact a perfect saint. That is repentance is that hard and that easy. It is a thought. But a thought with that much power and conviction that in fact one never repeats the sin. It has little to do with what most people think of as repentance. If you want to see proofs in the Torah for this I suggest reading the book Gates of Repentance by Rabanu Yona where he bring Biblical proof.