Does a divorce occur by saying "she is divorced" with the intention of frightening the wife, or by writing "divorced" on marriage websites, while being ignorant that this could cause a divorce?

As long as you did not intend to divorce your wife, but rather wrote the word "divorced" intending to lie, then no divorce has occurred to your wife by this writing. This is because the preponderant opinion is that a divorce does not religiously occur for someone who falsely states that he has divorced his wife. However, informing the woman you wish to marry that you are divorced, while in reality you are not, is a lie and deception, which the Sharia has forbidden, based on the saying of the Messenger of Allah, peace and blessings be upon him: "...and whoever deceives us is not of us."