so when someone run node, he can keep his wallet on his network instead of others wallet like freewallet, btc, and ... ?
When you run a node, you become a part of the Bitcoin network. This means that you need no third party to transact. Your node will only receive and verify blocks. Once you want to broadcast a transaction, you'll send your raw transaction to nodes that will then share them to other nodes. Hence, peer-to-peer network.
As for this question:
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Is running a Bitcoin node profitable?
I'd say no, if you're referring to money. If you run a node, it doesn't mean you'll be rewarded with bitcoins. You'll have to help the network for that, by mining. But, to me personally, it's a profit staying private, with no need from a third party.
A third party can be anyone you'll require to transact funds. It can be CoinBase or just an electrum server.
