What would be the baking time change and temperature change if using an 8 inch round cake pan instead of 9?

You have two options - you can either reduce the oven temperature by 25 degrees, or keep it the same; either way, check it about 10 minutes sooner than you normally would, and don't pour all the batter into the pan, so it doesn't overflow in your oven.

In general...and this goes especially for baking...its a very good idea to learn to recognize when something is done without relying on time/temp. Often, with variables such as weather, humidity and altitude, baking times vary wildly with any given temperature. The minute i began to know what "done" was, or as close to it as I possibly could manage, was the moment my cooking changed forever.

in the case of temperature, you don't need to change temp. Just adjust your cook time. with the smaller pan it will be a tad longer, however not much... like by 5 or 10 minutes. Check back of a store bought cake box, they generally have various cook times for different size cakes like cup cakes take less time to cook that 8 or 9 in pan vs 13 by 9 etc... I think the 8 inch will take a tad longer than 9 inch because wet mix is deeper/contained in smaller confines as appose to a larger pan spreading out the mix to cook more quickly

In general, you would lower the temp by 25° and start testing 10 minutes after the original time. You also need to be careful of overflow because of the size difference. I wouldn't use all of the batter. I also wonder if you need to change the size of the cutout of the blue cake. Personally, I would go purchase the 9" pan, but if you can't, then just go for it.

One inch isn't really all that much when it comes to baking time. The variability would be similar to cooking time one oven vs. another. The recipe calls for 35-45 minutes, so I'd start checking the cakes at 30 minutes and readjust based on how done they are at that point. They cakes will be a bit higher (because the pan is smaller) so I'd guess that it may be closer to 40 minutes.