The time and random tools use this browser. They do not ask a server for the clock, and they do not need an account. A laptop clock that is wrong will be wrong here too.
Unix Timestamp Converter treats ten digits as seconds and thirteen digits as milliseconds. Any other length is rejected. The UTC line and the local line are the same instant. Time Zone Converter reads a wall-clock time in the IANA zone you name and shows that instant in another zone. A daylight-saving gap is labelled rather than invented as a real local time. Epoch Now prints the current Unix time from Date.now and updates it while the page is open.
Countdown subtracts that same clock from a local date and time. A target that is already past shows Done. It does not show a negative count.
Random Number draws one integer between two bounds, and both ends count. Dice Roller, Coin Flip, and Yes or No use the cryptographic generator. A run of one face does not change the next draw. Yes or No does not read a question, and the word it shows is not advice. The draws are not stored on a server.
Tools
Read the privacy page for what each check sends.