1. How to make any home version as default on the website?

Open Home — Version 2, or Home — Version 3 settings panel and click button «Made»

2. How to make Category Links centered on the Category Page?

Choose Categories block and add combo class «Centered»

3. How to make centered Header on the Category Page?

Go to Home — Version 3 page.
On this page Header block has combo class «Version 3»
Click on the Header block with right click.
Menu will appear and then choose Copy.
Go to Categories Template and paste into the Body.
Remove old Header.
Drag new centered Header to the top.