'\u0000' is a valid char. Its bit value is 0000_0000_0000_0000, and it is called the null character. You can find it on this Unicode chart.
You initialise a char exactly the same way you initialise anything else; put it to the left of an assignment operator (=) and put a char literal or an expression which is convertible to a char on the right of that, then a ; sign.
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