For the first part, try

echo Aa | od -t x1

It prints byte-by-byte

$ echo Aa | od -t x1
0000000 41 61 0a
0000003

The 0a is the implicit newline that echo produces.

Use echo -n or printf instead.

$ printf Aa | od -t x1
0000000 41 61
0000002

xxd is a hex-dump utility shipped as part of the vim-common package
It has a handy -p option which outputs a continuous 'plain/postscript' hexdump style.. This can easily be reversed via -r... -u will output upper-case Hex-Digits.

$ echo -n "M" |xxd -p    # 1 ASCII char= 1 UTF-8 byte; Unicode Codepoint: U+0041
4d

$ echo -n "〶" |xxd -p -u # 1 CJK char= 3 UTF-8 bytes; Unicode Codepoint: U+3036  
E380B6

$ echo -n "Dump a string" |xxd -p -u  
44756D70206120737472696E67

$ echo -n "Dump and Revert" |xxd -p |xxd -r  
Dump and Revert

You have several options

$ printf hello | xxd
0000000: 6865 6c6c 6f                             hello

See also: Ascii/Hex convert in bash

This code will convert the text 0xA7.0x9B.0x46.0x8D.0x1E.0x52.0xA7.0x9B.0x7B.0x31.0xD2 into a stream of 11 bytes with equivalent values. These bytes will be written to standard out.

TESTDATA=$(echo '0xA7.0x9B.0x46.0x8D.0x1E.0x52.0xA7.0x9B.0x7B.0x31.0xD2' | tr '.' ' ')
for c in $TESTDATA; do
    echo $c | xxd -r
done

As others have pointed out, this will not result in a printable ASCII string for the simple reason that the specified bytes are not ASCII. You need post more information about how you obtained this string for us to help you with that.

How it works: xxd -r translates hexadecimal data to binary (like a reverse hexdump). xxd requires that each line start off with the index number of the first character on the line (run hexdump on something and see how each line starts off with an index number). In our case we want that number to always be zero, since each execution only has one line. As luck would have it, our data already has zeros before every character as part of the 0x notation. The lower case x is ignored by xxd, so all we have to do is pipe each 0xhh character to xxd and let it do the work.

The tr translates periods to spaces so that for will split it up correctly.

echo -n 5a | perl -pe 's/([0-9a-f]{2})/chr hex $1/gie'

Note that this won't skip non-hex characters. If you want just the hex (no whitespace from the original string etc):

echo 5a | perl -ne 's/([0-9a-f]{2})/print chr hex $1/gie'

Also, zsh and bash support this natively in echo:

echo -e '\x5a'

Though short, @Juergen comments that this answers his question. Use the following:

printf "%X\n" \"A\"

Note, this provides the single-byte ("ASCII", UTF-8) charcter code. See the Unix & Linux StackExchange for more on char -> hex value and the converse, hex -> char, using bash shell and/or python.

perl -e 'print ord("_"), "\n"'

In general, the shell could understand hex, oct and decimal numbers in variables, provided they have been defined as integers:

$ declare -i v1 v2 v3 v4 v5 v6 v7
$ v1=0112
$ v2=74
$ v3=0x4a
$ v4=8#112
$ v5=10#74
$ v6=16#4a
$ v7=18#gg
echo "$v1 $v2 $v3 $v4 $v5 $v6 $v7"
74 74 74 74 74 74 304

Or they are the result of an "Arithmetic Expansion":

$ : $(( v1=0112, v2=74, v3=0x4a, v4=8#112, v5=10#74, v6=16#4a, v7=18#gg ))
$ echo "$v1 $v2 $v3 $v4 $v5 $v6 $v7"
74 74 74 74 74 74 304

So, you just need one way to print the character that belongs to a variable value.
But here are two possible ways:

$ var=$((0x65))
$ printf '%b\n' "\\$(printf '0%o' "$var")"
e

$ declare -i var
$ var=0x65; printf '%b\n' "\U$(printf '%08x' "$var")"
e

The two printf are needed, one to transform the value into an hexadecimal string and the second to actually print the character.

The second one will print any UNICODE point (if your console is correctly set).
For example:

$ var=0x2603; printf '%b\n' "\U$(printf '%08x' "$var")"
☃

An snow man.

The character that has an utf-8 representation as f0 9f 90 ae is 0x1F42E. Search for cow face site:fileformat.info to get it:

$ var=0x1F42F; printf '%b\n' "\U$(printf '%08x' "$var")"
🐮

Note: There is a problem with the UNICODE way in that for bash before 4.3 (corrected in that version and upwards), the characters between UNICODE points 128 and 255 (in decimal) may be incorrectly printed.

References

Fourth paragraph inside PARAMETERS in man bash:

If the variable has its integer attribute set, then value is evaluated as an arithmetic expression even if the $((...)) expansion is not used (see Arithmetic Expansion below).

Inside "ARITHMETIC EVALUATION" in man bash:

Constants with a leading 0 are interpreted as octal numbers. A leading 0x or 0X denotes hexadecimal. Otherwise, numbers take the form [base#]n, where the optional base is a decimal number between 2 and 64 representing the arithmetic base, and n is a number in that base. If base# is omitted, then base 10 is used. The digits greater than 9 are represented by the lowercase letters, the uppercase letters, @, and _, in that order. If base is less than or equal to 36, lowercase and uppercase letters may be used interchangeably to represent numbers between 10 and 35.