serial.write(0x00); gives an error

Actually, isn't the problem that the literal constant 0x00 is typed - but as an int?

No, it is not typed. However, in the absence of directives the the contrary, literals that can be interpreted as ints will be. Whether the value fits in an int, or not. The problem is that the literal can be interpreted as an int, but there is no write() method that takes an int, so the compiler needs to be told more information, so it can choose the right overloaded method to call.