It's not clear what you mean by "inside a full node".
Usually when you use Ethereum you have a number of nodes, which talk to each other and agree on a blockchain, which represents an agreed history, and thus an agreed database.
A blockchain can be public, such as the Ethereum main network or the Ropsten test network, consisting of an arbitrary number of nodes talking to each other and producing the Ethereum blockchain or the Ropsten blockchain respectively. It can also be private, consisting of a number of nodes that you have set up yourself or with your friends and connected to each other, producing your own blockchain.
In an extreme case you could have a "network" consisting of a single node, which runs its own blockchain, and doesn't talk to any other node. This is often how people do development.
Once your node is connected to a blockchain, whether a public network, a private network or a single node, it can create accounts and make transactions between them. Changes you make to these accounts will be shared by any node using that blockchain.
The fees will depend on the blockchain you are using; If you are using the main public Ethereum network, your transactions won't be processed by the network unless you pay fees. If you are using the Ropsten test network, you will need Ropsten "ETH", an otherwise worthless currency recognized by miners on the Ropsten test network. If you're using your own private network, you have your own version of "ETH" that you create yourself and nobody considers valuable, and you can use that for fees.