Yeah you can . You don't have to take out the sim . You can just connect to wifi and use Internet . Of course no calling or texting unless you have the textfree app or such until the phone is back on .
Yes you can, you will simply need to insert your newly activated sim card or the previous one into the old phone. Next, you will have to connect the phone to a PC and activate it on iTunes over the internet, after which you can use the device as an iPod touch.
All that is needed for most apple products, such as your iPhone, is a wifi network. Phone service is needed to place calls, unless they are FaceTime chats, however. Also, as stated above, texting needs an app to text via wi-fi