I'm no expert at Easy Paint Tool Sai, but lines generally tend to look smoother if you create a vector layer rather than a normal layer. Vector layers might be easier to work with if you're using a mouse. Improving resolution can help as well, but sometimes they cause the file size to be massive.
It makes a difference. If you simply try to change the resolution to print at 300 after making the work in 72..it will not look good. Compare it to taking a low res image from the internet and trying to make even an 8x10 out of it. It will look pixelated. Even if you have no intention of printing the image it is still better to work bigger and downsize after. Your image will be much crisper and details will stand out more. The lines do appear smoother when working with a higher DPI simply because it's more dots per inch, resulting in a clearer picture. Most digital artists will recommend about 300 DPI/ resolution for working in.