You will probably get lots of different answers from different people! So this is a great way to try and put everything together
1. Are certain ponies more susceptible to cancer than others? I've seen it on a lot of Big Brothers (especially Barnicle), but I've seen plenty of earlier ponies (Minty, Applejack, etc.) that had nothing.
Yes, I certainly believe some plastics are more prone - the BB as you mention, the second edition rainbow ponies, Gingerbread from the TEs, the Mountain Boys Thundercloud & Sunburst, Starshine from the Regenbogen set [she is one of the worst!], Ringlets from the Brush n Grow set, Baby Graffiti from the Peek A Boos, TAF Nightglider
2. Are there any examples of non-G1 ponies having cancer?
As cancer is a result of ageing plastic, I dont think any G2, G3 are old enough to as yet have such a breakdown and then discolouration of plastic - its possible, but I dont recall anyone ever coming across an actual example
3. This is more of a think-about-it, it's-your-opinion question: do you think that the change in plastic in non-G1 ponies will protect ponies from cancer (either forever or temporarily)? Remember the G1s have perhaps the softest plastic, and all generations after are considerably harder.
Do you mean do you think later gens will not have problems because they are made of a different plastic? No - all plastic is subject to ageing no matter how it is manufactured as ageing = breakdown. And over time all plastic will breakdown. The slightly different plastics may mean they age/breakdown slower or in a different way but they will still age over years or decades.