1. It is not true that you cannot sync a blockchain if the process is interrupted. Actually you can stop the process at any time and continue later, even if there is a power failure. If syncing is stuck, then you should get help from people who provide support for bitcoin core, such as the channels listed here: https://bitcoin.org/en/bitcoin-core/help I would also recommend that you study your log file.
2. The image was probably too high resolution and was not posted (says “File exceeds allowed file size.”, so I cannot see it.) You can either use
rpcauth to define the username and password that your wallet should accept over RPC connections. Then, enter the same password in the coin adapter’s RPC settings. Then, go to the coin adapters screen and see what error message you get under “Status”. If yuu let me know what error message you see in that screen I can help you.
3. The plugin needs to connect to the wallet, not the other way around. So the plugin’s coin adapter needs to know the IP of your wallet. In your wallet’s conf file, you need to specify the IP of the WordPress machine, so that the wallet can expect these connections and allow them. When the plugin recommends your conf file entries, it tries to guess the IP of your WordPress machine. This guess may be wrong, so enter the actual IP of your WordPress web server instead. If it is a home IP then obviously the web server will not be able to communicate with your wallet. (Unless if you have the skill to configure your router using NAT.) This is something that I cannot help you with. In general, even if you decide to run your wallet on a VPS, you need to think about HOW your WordPress maching is going to start a TCP connection to your wallet. This means that you need to think about routing and any firewalls that are in the middle.
4. I am not certain if the extension is what you need for your use case. This plugin is not built for selling tokens or mining contracts. If what you need is an exchange, then the Exchange extension is for you. You could mine coins, deposit them to a user on your site, then place sell orders at various prices, and others can login and buy your coins with Bitcoin. Additionally, you can have markets where it is only possible to buy or only to sell, so perhaps you could use this feature. But first you need to connect to a wallet.
In general I believe that it is possible to run your wallet at home IF you know what you are doing very well, that includes setting up networking. For most people it’s best if they install a full node on a VPS.
Hope this helps.