Some clarifications

1.The auction items are nodes and commerce products. Correct?
- no. they are nodes. the Commerce part is in fact secondary to be able to process a cash value against the Auction ID created in the node.

So it means if we do not install auction commerce module, then we cannot have payments on the site and it will be an auction just for display purpose where no actual transaction takes place. Hope you got my point. Just trying to understand the functionality of this module.
- the Auctions Commerce module is a separate module so it could be superseded by some other "processing module" if indeed you didn't want to use 'Commerce' for whatever reason.. (and something else is available to use..). yes. you would have to custom integrate. which is why Auction Core is its own module as well.

2. For example if someone wants to create a site like ebay, is it something this module can do? You can also give other real life examples
-yes, ebay would be a 'Commerce processor' or somethings like that.... (if ebay provides that service themselves, i'm not sure if you are proposing something theoretical yourself. i don not have any experience with 'ebay tools', as a developer..)