Your questions are very important as in this age of advance technology many Muslims recite Quran from the web and computer. Iphone has made even easier for every person to carry the whole Quran in his pocket and made it convenient to read from it.
At this point many people seem to have similar questions with regard to touching the screen etc...
I will answer your questions below to the best of my ability Insha'allah:
1- One is not required to be in the state of Wudhu if he wishes to recite Quran without touching the Mus'haf as long as one is not in the state of Janabah (major impurity). So, if one reads the Quran off of the monitor then Wudhu is not required though it is better to have Wudhu.
Similarly, if one wishes to read Quran off of the screen of a handheld device such as an iphone/ ipod or any touch screen then Wudhu is not required as long as one does not touch the part of the screen which appears to be above the letters.
2- If one reads Quran from a touch screen device such as an iphone/ipod then it will be fine as long as one refrains from touching the part beneath which the letters appear.
The Ulama may have a difference of opinion with regards to this particular ruling. However, I feel that it is safer not to touch that part of the screen which is right above the words of Quran without having Wudhu.
3- You may write the name of Allah or the Verses of Quran on your text messages/emails without any reluntance as long as the text/email remains in an electronic form because even if the device is placed on the ground, the actual text will never be considered on the ground just as if a Hafiz falls down or lies down on the floor while he has the entire Quran in his memory.