The md5sum of “nothing” (a zero-length stream of characters) is d41d8cd98f00b204e9800998ecf8427e, which you’re seeing in your first two examples.
The third and fourth examples are processing a single character. In the “echo” case, it’s a newline, i.e.
$ echo -ne '\n' | md5sum
68b329da9893e34099c7d8ad5cb9c940 -
In the perl example, it’s a single byte with value 0x00, i.e.
$ echo -ne '\x00' | md5sum
93b885adfe0da089cdf634904fd59f71 -
You can reproduce the empty checksum using “echo” as follows:
$ echo -n '' | md5sum
d41d8cd98f00b204e9800998ecf8427e -
…and using Perl as follows:
$ perl -e 'print ""' | md5sum
d41d8cd98f00b204e9800998ecf8427e -
In all four cases, you should expect the same output from checksumming the same data, but different data should produce a wildly different checksum (that’s the whole point — even if it’s only a single character that differs.)