echo '0A' produces three characters: 0 A NL; xxd -b will then print those three characters in binary. If you wanted just the single byte whose value is 10 (i.e. hexadecimal A), you could write (in bash):
echo -n $'\x0A'
^ ^ ^
| | |
| | +-- `\x` indicates a hexadecimal escape
| +----- Inside a $' string, escapes are interpreted
+------- -n suppresses the trailing newline
A better alternative would be printf '\x0A'; printf interprets escape sequences in the format string, and does not output implicit newlines. (For a completely Posix-compatible solution, you would need an octal escape: printf '\012'. printf should work on any Posix-compatible shell but hexadecimal escapes are an extension.) Yet another bash possibility is echo -n -e '\x0A'; the (non-standard) -e flag asks echo to interpret escape sequences.
echo '0A' | xxd -b won't output the equivalent of hex 0A, because xxd doesn't know that you intend 0A to be a hex number rather than two characters. It just takes its input as a series of characters, regardless of what those characters are.
Endianness does not affect bytes. The order of bits inside a byte is entirely conceptual until the byte is transmitted over a serial line and even then it is only visible with an oscilloscope or something similar.
