Is it legal to own and operate a website that would host database leaks, accounts lists, Anarchist's Cookbook (guides on making bombs etc, drugs and more), and guides on stealing credit card info and other things such as DOXing?
It depends on the jurisdiction and information.
A guide to making bombs would be prima facie illegal in the UK per s58 Terrorism Act 2000 http://www.legislation.gov.uk/ukpga/2000/11/section/58, for example.
You ask about a number of different types of material:
The Anachist's Cookbook would be considered to be material helpful for terrorism, and hence illegal to possess, never mind distribute.
Other how-to guides for crimes would probably be considered to be encouraging or assisting a crime, which is an offence in English law.
Having a database of leaked information is not illegal in itself, but if it contains credit card data or passwords and there is an intent to use these fraudulently then it would be "an article for use in fraud" and hence illegal under the Fraud Act 2006. Providing information from the database in a form that could be used for fraud, especially in conjunction with guides on how to do so, would be "encouraging or assisting a crime". The operator might also be charged with conspiracy if there is evidence of a specific relationship between the operator and another criminal, such as selling access. There may also be copyright issues with distributing it.