Built in your browser from your device's cryptographic random number generator. Nothing is transmitted, logged or stored.
Characters come from crypto.getRandomValues, the browser's cryptographically secure generator, rather than Math.random. Indexes are drawn by rejection sampling: any raw value landing in the uneven tail of the range is thrown away and redrawn, so every character in the set is equally likely. One character from each set you tick is placed first to guarantee the mix, then the whole thing is shuffled so those positions are not predictable.
The entropy figure is length multiplied by the base-2 logarithm of the character set size — the number of bits an attacker would have to guess through if they knew your exact settings but nothing else.
On this page the work happens entirely in your browser: there is no request carrying the password anywhere, and nothing is stored. You can confirm that by opening your browser's network tab while you generate one.
Around 75 bits comfortably resists offline cracking today, and anything past 100 is far beyond current reach. A 16-character password using all four sets lands near 99 bits.
Because a password you have to read aloud, copy off a screen or type from a printout is easier to get wrong when l, 1, I, O and 0 are in play. It costs a little entropy and buys accuracy.
Yes. A long random password is only useful if you never have to remember it, and reusing one across sites undoes its strength entirely.