Are we witnessing the opening of Daniel's book today?

Yes. Daniel was told to shut up the words and seal the book until the time of the end, when it would be opened. The passage states that we are certainly witnessing that opening today, as its end-time scenarios are now being understood.

Les explains that Daniel's prophecy was sealed until the time of the end, making it a closed book that was almost incomprehensible to many scholars and theologians throughout history because it contains so many end-time scenarios they could not understand. He points out that Daniel was told the book would be opened at the time of the end, and he asserts we are certainly witnessing that opening today. Les also connects verse 5's "many shall run to and fro" and increased knowledge to the end time, including the explosion of technology.

Daniel 12:4

But thou, O Daniel, shut up the words, and seal the book, even to the time of the end: many shall run to and fro, and knowledge shall be increased.

When would the book of Daniel be opened up?

The book of Daniel was to be sealed until the time of the end. The Lord told Daniel to shut up the words and seal the book even to that period. It remained a closed book through history because its end-time scenarios were not comprehended. It would be opened up at the time of the end, which is witnessed today.