How to make a list of new test cases?

All test cases have a default execution result of Not Executed, so you can filter for those test cases in reports and dashboards.  You will probably have to use other filters to narrow down which test cases you want to show and there are various ways to do this using things like the folder structure of test cases if you want to limit to a function, or test cycles if you want to limit to a group, or test plans if you want to limit to a whole test stage - it all depends how you have structured your test library.  There are also other options that you will find in test cases and test cycles, e.g. labels, test case status, etc., etc.

There are limited options of information to show in dashboard gadgets but Reports can show more details, and if you export report data, you will get even more information.