Kernel execution and open tab dependency

I was wondering how the executing kernel depends on the tab that is open that e.g. displays the output of the currently executing cell.

From what I’ve read, closing the tab should not interrupt the execution of the kernel. But I have a cell that executes for a long time.
When I close the tab and reopen it, the output generated by the cell does not seem to “reconnect” to the cell in the sense that the output is printed in the box underneath the cell.
Also, normally the tab warns you before closing it when a cell is executed, but sometimes it also doesn’t?

And what happens if I change the code in my IDE, and the following appears,

Notebook changed
The notebook file has changed on disk since the last time we opened or saved it. Do you want to overwrite the file on disk with the version open here, or load the version on disk (reload the page)?

For now I just cancelled, fearing that hitting Reload and Overwrite will cause a similar problem to closing the tab where the output is not shown under the cell anymore, or even worse, the Kernel is interrupted or even restarted? Is my fear justified?

Thanks for your answer