Connecting a wallet, browsing, drafting a coin and signing in are free. There is no MemeWarzone fee to launch a coin.
You pay network fees for each transaction. Trades on the bonding curve carry a 2% fee, shown in the quote before you confirm. Making your own first buy at launch is optional and costs the coin price plus that 2% fee.
On Solana, setting up a new launch costs about 0.006 SOL in rent for its curve configuration, on top of network fees.