Someone without authorization made a false website about my business. What are my options?
Hire a lawyer and send a cease and desist letter. If they do not take the website down then, if you can prove they have damaged your business, you can sue them. It may be cheaper to try to buy it from them. This is why professionals tell you to 'BUY YOUR NAME'. the same applies to business names. If you open a cleaning business called ZaaZaaZipZoodle and then a year later you go to build a website and you see someone has a website about throwing dog poo and it is ZaaZaaZipZoodle...they bough for and paid for the name and the website so you would have to buy it from them. If they refused to sell then you would have to go and reserve ALL of the similar names and then launch a SEO and Marketing campaign to drive the website that has your name down in the rankings while you pay to have the website you create for your self (ZaaZaaZipZoodie) promoted. You can change your company name OR buy the domain in Dot net, Dot USA, Dot corp extensions and heavily advertise those. Eventually the people who own 'your' domain' name will get tired and let it expire and then you can snap it up. Message me and i'll give up a few more pointers.
If you want to sue them, consult a lawyer. You have no control over someone else's website. A lawyer might get it taken down.
Just posting a similar website wouldn't be a crime... I don't really understand the issue here though. Buy a domain, find a host and get your website active. The fake one will end up deprioritized by search engines as less useful.
Probably none. Courts have ruled that companies do not own websites until they actually register the name. Unless the web site you found is engaging in some action detrimental to your business, there is probably very little you can do. However, you may want to spend the $200 fee to have a lawyer write a cease and desist letter to the owner of the website asking him/her to remove any reference to your business - that maybe enough to scare him/her.
Did you hire a company to do the website? If so, did you ask them about the situation? Based on the little information that you have provided, I would guess that they were doing a sample that accidentally got released.
"What are my options to remove it?" You can offer to buy the domain name from them (which is why people do this). Or you can write to them and tell them that you will never, ever buy the domain name from them (and hope that they believe you and decide to stop paying for it themselves).