Assume I installed my personal bitcoin full node through Bitcoin Core wallet and connected my Sparrow wallet directly to it. Is that the right direction or am I supposed to connect my wallet to a public server instead?
You can participate in in Whirlpool only if you run full node with Ronin Dojo node package.
Sparrow is using same pools like Samourai wallet, they are just another client, and I would always choose Wasabi coinjoins rather than what Samourai is doing, but you can find detailed instructions on sparrow website.
I would wait for Wasabi 2.0 to come out soon, it should be more simple to use and I here some great improvements are coming, like reducing 0.1 BTC minimum.
How do I properly configure my bitcoin full node? What further steps should I take to achieve maximum anonymity?
There are many guides for running full Bitcoin node and it's nothing complicated, all you need is to have separate computer of RaspberryPi with hard drive, than you download entire Bitcoin blockchain, and let it run.