Can I change from a 7 to a 9 speed cartridge without changing the derailleur?
Absolutely not. You will need a new rear shifter and derailure, as well as a new rear hub. You can use your existing rim, but you will need an 8/9 speed hub and also a 9spd chain. If you want to do it on the cheap, you can in fact keep your crankset and front deraillure, as well as the existing front shifter (I’m guessing it is a downtube shifter?) Shifting in the front will not be crisp, but it will work. If you have some spare change, go ahead and get yourself a new front shifter and front derailure, but you can still keep your crankset. They are expensive and the one you have will work fine. I did it myself when I got my first road bike ten years ago, and don’t let anyone tell you different. If you really want to save money on this thing, get your parts on ebay. If you are looking to spend a little more, consider going to your local bike shop and seeing what they have on sale. Last year I got a $3600 bike for $2200. Thats a pretty high end bike, but you can find a more entry level b