I noticed that I can run a node with Bitcoin Core.
If I open my computer always and make the full node run on my device, what benefits can I get? Is there any reward for serving this?
No, full node operators are not compensated in any way. If you run a full node, you will receive no monetary benefit.
However running a full node does benefit you. It means that you are contributing to the network's security. Your full node is verifying and relaying valid blocks and transactions so you are contributing to the transmission of blocks and transactions and ensuring their validity. This then corresponds to your node contributing to the health of the network and helping the network stay alive.
Furthermore, a full node allows you to have privacy and security in your transactions. Because a full node fully verifies every block and transaction, when you use it as a wallet (or have a wallet that is connected to it), your transactions are guaranteed to be valid and there is almost no possibility that you can be defrauded (assuming that your node is well connected). It also gives you more privacy as there is not one server or node that is giving you data as with SPV wallets.