If you purchase songs on your iphone, then sync it to your computer, will all the songs you purchased on your phone be deleted and replaced by the songs in your itunes library?

First of all if you are really worried when you connect the phone to your computer go to the device summary page in iTunes and change to manually manage the device so that you are in control of what goes on to it.

A synch will transfer purchased items from device to computer and they are always available to re-download from 'the cloud'. Once you have the songs on your computer I do suggest that you burn them to CD or back them on to an external hard drive as sometimes items are withdrawn from iTunes so you can no longer re-download. Indeed the terms and conditions we are all accepting today with the IOS7 update specifies that it is our responsibility to back items up.

So as long as the songs you have already purchased are still available on iTunes, you can download them again should they disappear.