All the NFTs successfully purchased on the KleverNFT DEX Marketplace are yours. When you buy an NFT with a fixed price or instant buy price, the NFT is yours. When you make a Bid for an Auction NFT, you will need to wait until the end of the Auction and be the Auction winner to be the new owner of the NFT. Once the auction ends and you are not the auction winner, you must claim your NFT bid.
Differently from the Launchpad, when you don't still have custody of your wallets, on the DEX, you connect your wallet and process everything directly on-chain and with your wallet.