If you want decentralized one: bisq.network or robosats.org

Read more for some other ones here: https://kycnot.me/service/robosats

For centralized and requiring KYC, it depends on your country. Binance, Bybit, Bitget are common ones. Coinbase for people living in United States.

I can recommend Foundation Passport. Trezor is not also bad. That are both open source wallets.

You mean any address generated from the same seed phrase on the wallet can be used? Yes. It is even advisable not to reuse address.

I do not know for altcoins, but for bitcoin it is not possible. Although, it is possible theoretically but not possible with the hash rates bitcoin miners are generating and with how a single mining pool does not have up to 51% hash rates. Even miners know that the bitcoin mining will be profitable for them than to attack the blockchain where they are earning money.

Cold wallets (also called offline wallets). Example are wallet on an airgapped device like this one and airgapped hardware wallet like Foundation Passport.

Pick tier 1 exchanges in lists given by Coinmarketcap or Coingecko but remember that centralized exchanges are dangerous for storing your bitcoins there.

Good hardware wallets must be non custodial and open source.
[LIST] Open Source Hardware Wallets

To receive bitcoins, you have to let the sender knowing your Bitcoin public address. In HD wallet, there are many addresses and you can share one of those addresses to the sender.

Learn more about HD wallets.
https://learnmeabitcoin.com/technical/keys/hd-wallets/

Bitcoin blockchain has never been 51% attacked.

Cold wallets, and hardware wallets are cold ones.