Do you need to send them a finished, edited version of your book? No. Since you'll probably be on a tight schedule, it's okay to send the manuscript before it has been visited by your editor. Just be sure to let the reviewer know that the text is going out for editing at the same time so they may find some typos, etc. in the manuscript. You don't want them to think that the finished product will have errors or they may decide not to send you a review.
How do you get well-respected, busy, and perhaps famous people take the time to read your book? Ask them several months prior to publication so that you have plenty of time, but give them a deadline a month or more (if possible) before you need the review. There are always one or two people who take forever and need numerous reminders to write their comments. Make sure you make the deadline date clear! It's amazing how many people will forget and wait until the deadline is past. It's also a good idea to give a follow-up call a week or so after you mail the manuscript to make sure they've received it. There's nothing worse than waiting a few months for a review only to find that your reviewer never got the book. You've just wasted two precious months!
When you ask them, mention where your book will be sold, tell them it will mean national exposure for them/their business. In short, sell them on the idea of writing the review, saying it will help THEM. It also helps if you tell them you only need a few sentences to a paragraph. Readers don't expect longer review quotes inside the book.
Once you have the quote, DO NOT change the text, or reword it in any way with the exception of fixing typos. If there is a problem with the quote (perhaps a character was mentioned in the wrong context), contact the expert and ask their permission to fix the error (although it's best not to use the word "error."). Set the quotes up so that you have the quote followed by the expert's name and his/her claim to fame (business, award-winning author, etc.). Readers will be very interested in these quotes and they DO help sell books!