1. Are you expected to be the expert on everything? No - Good engineers continue learning. You can never know everything and anyone that claims they do is wrong.
2. In your opinion should you be to be an expert in all of those subjects? No, If I don't know, I would ask an expert with years of experience in their niche.
3. Is it ever acceptable to tell the boss/customer that you would have to do some research before completing the project? No, I would just get it done but give an approximate deadline once you know how much time it will involve.
4. If you do need to do some reading then is there one book/website that has all the answers? (other than Wikipedia and the Mechanical Design Forum) I would not trust Wikipedia! Maybe find a specialist company and look at their blog and youtube channels? Alternatively, look on google?

 

Hmm, you see, I think the exact opposite. I hate it when people don't know an answer but try to bluff it anyway.

I'd MUCH rather people told me, "I don't know but I'll get back to you with the answer"