The Fourth Amendment says "nor shall any person [...] be deprived of life, liberty, or property, without due process of law". I don't see any process of law here. The FBI is law enforcement, not judicial.
Are police officers or FBI agents who are being shot at prohibited from shooting back at their attacker, because that would deprive life without due process of law?
Can suspects not be arrested until a court case has exhausted all its appeals, because that would deprive liberty without due process of law?
The FBI (presumably) had a warrant here, after gathering evidence, and the cooperation of various other agencies including a few district attorneys. The US (hopefully) is a land in which the process of acquiring a warrant before actually seizing anything or arresting anyone is so commonplace that it isn't even mentioned. There was a process of law, it involved the courts, you didn't see it because it didn't need to be mentioned, and it didn't involve the completion of a criminal case.
(There are separate safeguards, against police officers killing people without reason, arrests happening without a warrant, or liberty or property being deprived for unreasonably long while a court case is artificially stalled. Some of those safeguards are not as effective as a free people would hope. But I don't think that's what you were referencing, and I don't think you can make a case that any of those happened here.)
That is not true any more. There was a discussion [1] two months ago about the changes in the law regarding property seizure post 9/11. They call it "asset forfeiture".
The FBI clearly would have sought a warrant from the judiciary as they would in any other case. I really don't understand where you're coming from here. There is nothing unusual at all about how all of this has gone down.
If you read through the criminal complaint filed against Silk Road 2.0 / Benthall, they establish pretty sufficient probable cause for a search and seizure.
Arrest warrants for the individuals involved is a separate process.
Selling drugs is illegal. Hence running a website to sell drugs is also illegal. Of course the government is going to shut down the website or any other sites where there is clear evidence of criminal behaviour. The criminal case against Blake et al over whether they ran the site is a separate issue.