The Apache license allows a derived work to be published under a different license and "retaining copyright and license notices" does not mean that all copyright notices must be in chronological order next to each other.
Thus, you can write the header of the file like this:
* Copyright 2020 Cool company. All rights reserved.
* < Your ...
As I understand your question, you have written a server that offers a subset of the functionality of Apache Tomcat and you based your design on a book that describes the design principles of such a server (using Apache Tomcat source code as illustration) and using some libraries you took from Apache Tomcat.
The Apache 2.0 license is a permissive license ...
You have found unmaintained software, distributed under Apache2. You wish to update it, and to distribute the modified, derivative work under GPLv3/AGPLv3 (you are unclear as to which). You want to know if this is permitted.
My belief, about which I have written elsewhere, is that one can take a piece of existing software under licence A (which permits re-...
If my code is written in Python, can I re-used the abandoned software as a module (released under APACHE-2) and add my wrapper under GPL-3?
As the two licenses are compatible, you can indeed use the Apache-2 licensed code as a module in your GPLv3 licensed code.
The same holds true when you use the AGPLv3 instead of the GPLv3 or when the third-party module ...
If their code appears in your repository, it will be helpful to anyone that needs to go through your old commits to have that author information available to them. However, you could probably get away with just mentioning them on GitHub, rather than mentioning them in your license since they didn't make the final product.