I was on Nuvaring for quite some time and really liked it. I have recently switched to Yasmin because the progestin in it is a better fit for me (sadly).
First off, I want to say how terribly sorry I am to hear about your mother. I can relate to how hard that is. That being said, there are no studies that indicate there is an increased risk of cervical cancer with Nuvaring as compared to the pill. Most cervical cancer is believed to be caused by HPV, which supposedly nearly everyone gets at some point. The BEST way to prevent cervical cancer is to get annual pap smears. Cervical cancer develops very slowly, and cellular changes in the cervix that are found on a pap can easily be treated before they ever develop in to cancer and your paps will return to normal. Up until a few years ago, mild cellular changes were not found with paps, but now they are very sensitive and are more likely to find very mild changes. You have good reason to be concerned, but even if at some point you have an abnormal pap, be glad that you caught it and can have it treated.
Side effects are similar to those with the pill. You will probably go through an adjustment period where you get breakouts and such, but you should adjust to it. But like with every hormonal method, not every woman tollerates each brand the same. So you may find in 3 months you love it, or you may find it doesn't work so well for you.
As for switching, it will likely be similar to starting it for the first time. You might have breakouts, mild cramping, breast tenderness, etc. Or, you may notice a change at all - part of it is going to be based on what type of progestin is in the pill you are currently taking - if it is a very similar form to the ring then you will probably find you have less side effects.
As for getting pregnant after the ring, its the same as the pill. You can potentially get pregnant as soon as you come off it, but your pre-bc fertility may take a month or two to return.