1. Do you ride Western or English?
2. Would you purchase tack (saddles and/or bridles) online?
All the time. Saddles too. Talk to the people before you buy and listen to their recommendations. Some shops will ask you to take measurements and send pictures. When I sent pictures of Mia's back to Dover, they recommended a less expensive saddle as being a better fit. Make sure you can return it if it doesn't fit.
3. How do you measure a horse for saddles and bridles?
Ask the store. Dover & DownUnder both asked for wither tracings and then pictures, and then said which saddles would fit, and which would not. They told me what information they needed and how to measure it.
One local tack shop - the largest in the area that I know of - told a customer that "All our saddles will fit every horse!" I haven't gone back. At the only place I know of selling English saddles, the salesgirl recommended a used 15" saddle...the owner then came running over and said it would be too small. No kidding - I later bought an 18" Bates online.
The online stores I've talked to had far more knowledgeable people to talk to than the stores I've been in where I live. They also had much greater selection, much lower prices, and would take returns without problem.