If someone unknowingly spreads a falsehood, does that person have the same responsibility for the consequences as someone who purposely spreads a falsehood? Why?

No.

Explanation:

The consequences are not as much about the falsehood as they are about the intentions of spreading it. You should teach someone the mindset that wouldn't spread lies, not just telling them lies are bad.

Depends. If it's a severe one and needs to definitely have an apology, then one should do it if they honestly didn't mean it. Misinformation can be deadly and spread whether or not its done intentionally or anything else. Instead of spreading misinformation, people should be helping and, if needed, expose the right people at the right time. If it's better not to say anything, then don't, but not everyone will follow the rules. So there is a great responsibility, especially casting into the unknown, but getting punished for it equally is a different story.

cyberstalking on the internet means to harass or stalk someone, a group, or an organization. this may include defamation, slander, and false accusations. in many jurisdictions, cyberstalking is a criminal offense. 

on the other hand, cyberbullying focuses more on intimidating, threatening or harassing someone. harmful bullying include posting threats, rumors, and sexual remarks.