In any case if I do so, then I hope I will be allowed to send the redeemed bitcoins from those sites to my Binance wallet, which is the only one which I want to keep...or?
Don't use Binance ''wallet'' or any other exchanges for keeping your coins, because they hold your private keys, so it's not really your bitcoin.
Use exchanges only for trading, and non custodial wallets for holding your coins, good open source options would be Electrum or Wasabi software wallets.
Hardware wallets are also good option but they are not free or perfect, and more important thing whatever wallet you use is to keep your private key or seed words safe.