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Not in this case, because the probably being estimated is "the chance a single page could contain a typo" and not "the chance the rest of the book could contain a typo."

To do the latter, you'd need to know the length of the book, yes.

In effect it does. If you have read 20 pages and found no typos you estimate the chance of an unknown page having a typo is 1 in 20/3. But if there is 0 unread pages then there 0 cases to apply the probability to. Make it 100 pages, then you have 100 cases each with a 1 in 20/3 probability. Of course if you read 30 more and still don't find a typo, it's now 50 remaining cases each with a 1 in 50/3 (estimated) probability.

Logically not, since your sampling method is imperfect and will not detect all typos and, in fact, some typos might make perfect sense given the context and be inherently undetectable forever.