Resizing the Branding Slider

Yes, it is.

All you have to do is upload a widescreen image. You can use the sample which came with the theme to make your image fill good in your slider.

Slider Sample: https://wp-themes.com/wp-content/themes/lupercalia/imgs/slider-sample.png

Then using some photo editor you can do something like this:

https://lh6.googleusercontent.com/QhU3fSyWA4fd2s7zkEaKRW1ZFGdTcz8o5pgiFokzW0tWO2ipVqxaPaAzWzZLxEMnVPbchf4tHFU

Or here

https://drive.google.com/file/d/0B2Nthhpwi5naUk5qLTBRYnNMb2s/edit?usp=sharing

How large is the size of the original slider to fill the whole screen’s width? I am trying to figure out what size my images should be as I want my slider to be much smaller.

It will fill the size of your screen, there is not a fix width for it.