You use Wordpress because you like the off the shelf parts.

You can make WordPress look like anything. It is PHP, so if you want you can have a page that is mostly a web App and just use WordPress for the content blocks on the page, but that wouldn't be the most efficient way to do things.

If you have to ask if it would be easier, then it would probably be easier.

Paying for custom design varies wildly. You could spend $50 on a kid in college who may or may not make something awesome. You could spend $50k on a major design studio.

As an SEO I saw both happen.