meaning - What does "customized website" mean?

Does, "customized website", mean:

1) a website with unique design and features

Yes.

2) a website that I can change, for example, add new page without writing a code.

No. That would be a customizable website. Not every customized web site remains customizeable after deployment. We happen to be customising this one as we type. But that changes the content. Not the design. We're also doing it after it was deployed.

Before being deployed EL&U had some customizations made. Among other tweaks it was given a different title, logo, and background color. Even the voting controls were changed. These were customizations. But as far as I know not a single line of code was changed. Just configuration.

The paragraph is asking for two customizations: the dashboard and the database. It is also asking that the site be easily customizable "to control my web[sic.] myself". This last feature already exists in other websites.

cus·tom·ize

ˈkəstəˌmīz
verb
past tense: customized; past participle: customized

modify (something) to suit a particular individual or task.

"the suit can be customized for every skydiving need"

google.com

If we were talking about clothing it would be simpler. Buy off the rack, get what they have. Go to a tailor, get a custom fit suit. The problem with websites is there is a whole confusing range between these extremes. The quoted paragraph is attempting to nail down where on that range the website will fall.

I can make, very cheaply, a site that says nothing but "Hello world". Having done it once I could offer it again even cheaper. But would anyone want that?

At the other end of the spectrum is a fully maintained actively developed website that can have it's design changed on a whim.

In between are the websites that allow content to change but are not actively developed so no code get's changed. These are deployed cookie cutter style: A shopping cart site. A blog. A stackexchange. The code is always the same but the content is different.

Slightly better are sites designed specifically for the customers unique needs. A custom site goes beyond content variations (my answer here is an example of content). A custom site respects the customers individual needs whatever they are.

Every choice to be different than anything that existed before costs time and money. Which is why the paragraph keeps asking what exactly they're getting for their money.