You can use a mixer for that or send your funds to an exchange with no KYC. But unfortunately only funds will be moved and the initial address will never disappear. Moreover anyone will be able to see on the blockchain which addresses have send funds to this address and also to which adress funds have been sent. So if you don't want to leave traces on the blockchain you must be careful. Or you should use anonymous cryptos like Monero instead.

For changing the wallet address, you can just use a SHW wallet like Electrum and select the change address option. However, this does not guarantee privacy though, because there's no way a Bitcoin is moved to another wallet address through the on-chain method that it won't show on the blockchain.
If you need total privacy, that prevents the connection between the old and new wallet where the BTC is moved to you'll need to use a privacy wallet or tumbler.

No, you can't do that. In the first place, there's nobody you can make a request to. If you custody your Bitcoin which was deposited to a certain address, nobody else but you who have complete control of your funds.

If you wish, you can mix your coins via a mixer or coinjoin, or you can trade them with privacy coins like Monero and swap them back to Bitcoin using an address you alone know.

But make no mistake, every time a transaction happens on the Bitcoin network, the blockchain indicates where the money is coming from and where it's going to. It can't just make funds disappear from an address without indicating where it's sent. If you really want this specific feature, you might consider moving to Monero or other privacy coins.