A nice book on the subject for you might be Volatility and Correlation from Riccardo Rebonato

Returns are distributed lognormally, because the stock price cannot go below zero and therefore the lowest return is -100%.

I don't see how arbitrage is getting MORE expensive, I'd actually say it's getting less expensive: Information is more widely available, so if anything, opportunities are more easily identified. Cost of trading is going down, so it becomes cheaper to take advantage of these opportunities...

This depends on the party who's trading... Do you mean fees for retail investors of for professional parties? As you can guess, the retail investors have to pay quite a bit more.

Don't buy the books, just get some good study materials. I can highly recommend the materials from Schweser (www.schweser.com)