When you are using a web part on a template, that web part's settings will be used on all pages that use that template. You cannot have different settings for the web part for each page that uses that template because the web part is part of the template, not the page (it's saved in the template data, not the page data). This is as it should be.

However, you can have dynamic variables in your settings if you use macros. You can use any contextual data available to you on each page in the where clause on the web part. If you need to, you can create a custom macro that you can pass a variable to that you can use to return the appropriate where clause for each page.

Keep in mind that you can use macro expressions for most settings of web parts to use the context to change the settings.

Being new to Kentico I recently had to solve this problem as well.

In my case I had created a Custom Table of information of a globe spanning companys offices wanting to show that information in global and regional pages.

The regional pages are based on a Region Map Template I created with a repeater listing offices in a region.

I did it by making each page a Map Document where that is a document type I created with a RegionID field. So each page knows its region.

Then in the repeater query WHERE clause I wrote:
office_table.region = {% RegionID %}

Thus restricting the query on office information to the documents region.