My iPhone 5 screen glass cracked?

I have a crack on my iPhone 5 screen, and want to get it replaced.
At most places, they charge 100~200 dollars to fix it. On eBay, I found this
http://item.mobileweb.ebay.com/viewitem?index=0&sbk=1&nav=SEARCH&itemId=400449814593
But I was wondering if this is what I need to fix it. It says that no touch sensor/digitizer is included. What does this mean?

Wi-Fi connection with iphone 5 without sim card?

I must admit that I do not know much about the iphones or any other smart phones. I would like to purchase an iphone 5. I do not intend joining any plans. I have broadband Wi-Fi at home. Can someone tell me if I can surf the internet at home or at hotspots ( eg. Starbucks, McDonalds ) with an iphone 5 without inserting a sim card.

Will Apple repair my screen the same day?

I have a shattered iPhone 5 screen & come to find out that apple is now offering a price of $149 to repair it. Will they repair the screen the same day? All answers are appreciated.