Answer to "How to Solder replacement headphone jack?"I hope that you have checked your headphones as well - mating connector on your headphones could be damaged. If you have to replace jack on your ipod , there is useful quide about how to solder with soldering iron at: http://www.soldering-store.com/soldering_guide/soldering_guid...
Answer to "Where can I buy de-soldering wick?"You can order de-soldering wick online at websites of any major distributors of electronic or soldering components. I do lot of shopping online at Digikey and I know that they have a wide selection of de-soldering wick in different sizes. Amazon.com has also good selection of desoldering wick. You can remove a lot of unwanted solder by placing your wick over solder and than heating desoldering wick with soldering iron.
Answer to "What soldering tip shall I use for soldering the display?"Use one of temperature controlled soldering iron with digital display such as Weller WESD51 soldering iron. That way you will be able to precisely control the temperature of iron to within 9 degrees Fahrenheit. There is soldering guide at http://www.soldering-store.com/soldering_guide/soldering_guid... Regards