You may assign '\u0000' (or 0). For this purpose, use Character.MIN_VALUE.

Character ch = Character.MIN_VALUE;

Does replacing a character in a String with a null character even work in Java? I know that '\0' will terminate a c-string.

That depends on how you define what is working. Does it replace all occurrences of the target character with '\0'? Absolutely!

CopyString s = "food".replace('o', '\0');
System.out.println(s.indexOf('\0')); // "1"
System.out.println(s.indexOf('d')); // "3"
System.out.println(s.length()); // "4"
System.out.println(s.hashCode() == 'f'*31*31*31 + 'd'); // "true"

Everything seems to work fine to me! indexOf can find it, it counts as part of the length, and its value for hash code calculation is 0; everything is as specified by the JLS/API.

It DOESN'T work if you expect replacing a character with the null character would somehow remove that character from the string. Of course it doesn't work like that. A null character is still a character!

CopyString s = Character.toString('\0');
System.out.println(s.length()); // "1"
assert s.charAt(0) == 0;

It also DOESN'T work if you expect the null character to terminate a string. It's evident from the snippets above, but it's also clearly specified in JLS (10.9. An Array of Characters is Not a String):

In the Java programming language, unlike C, an array of char is not a String, and neither a String nor an array of char is terminated by '\u0000' (the NUL character).

Would this be the culprit to the funky characters?

Now we're talking about an entirely different thing, i.e. how the string is rendered on screen. Truth is, even "Hello world!" will look funky if you use dingbats font. A unicode string may look funky in one locale but not the other. Even a properly rendered unicode string containing, say, Chinese characters, may still look funky to someone from, say, Greenland.

That said, the null character probably will look funky regardless; usually it's not a character that you want to display. That said, since null character is not the string terminator, Java is more than capable of handling it one way or another.

Now to address what we assume is the intended effect, i.e. remove all period from a string, the simplest solution is to use the replace(CharSequence, CharSequence) overload.

CopySystem.out.println("A.E.I.O.U".replace(".", "")); // AEIOU

The replaceAll solution is mentioned here too, but that works with regular expression, which is why you need to escape the dot meta character, and is likely to be slower.

Java strings are not null terminated. They end with the length in length. You can make a \0 the last character of a Java string, but that doesn't automatically terminate the string. The length of 12<\0>45 would still be 5 and not 2 as in C.

I'm going to assume you want to terminate the string at the first null character, as would happen in C. However, you can have null characters inside strings in Java, so they won't terminate the string. I think the following code will produce the behaviour you're after:

StringBuilder sb = new StringBuilder();
for (int i=0; i < mTypeSelection.length; i++){
    if(mTypeSelection[i] > -1) {
        sb.append(Character.forDigit(mTypeSelection[i], 10));
    } else {
        break;
    }
}
String result = sb.toString();

Converting the String to char array is an alternative. This works for me:

System.out.println(s.toCharArray());

Which outputs abcdef to the console (eclipse).