Is Bisq running on Bitcoin network? Because as Bisq was launching I saw these;
Connecting to Bitcoin network...
Synchronising with Bitcoin Mainnet (via Tor)...
It doesn't run
on the bitcoin network, but it syncs with it via Tor to fetch blockchain data and therefore improve privacy.
Since I now have my backup and seed phrase saved, am I free to use Bisq as a personal wallet?
You could, but even although it is non-custodial it is still a hot wallet, which are one of the least secure types of wallet. I would use it as a trading wallet, and move any funds you are not planning to trade to somewhere more secure such as a hardware wallet.
Since there is no KYC, if illegal activities are carried out on Bisq, is there a way government will trace it since Bisq doesn't have a CEO and not centralized ?
Since Bisq is ran peer to peer, a government cannot shut it down just like they cannot shut down bitcoin itself. Even if they take down the Bisq websites, then individual users can still run the Bisq client. And since there is no KYC or personal data collected, and everything is done via Tor, then Bisq don't have any information to hand over beyond what is already visible on the blockchain.
Why do most people not use this type of system that guarantees privacy, rather many people troop into centralized exchanges like Binance and even use it as wallets.
Greed and laziness are the main ones. People are too lazy to use the slightly more complex Bisq over somewhere like Binance, even although using Binance gives them absolutely zero security, zero privacy, zero ownership of their coins, and zero protection against scams. And of course people are greedy to put their coins in to high yield accounts or staking or some other nonsense which promises obviously unsustainable returns, despite dozens of such platforms going bankrupt or scamming over the past few months and millions of users losing everything.