Adding a TeX macro to the beginning of a file using sed (why doesn’t the method work?)

You have to escape the backslashes (so four backslashes will insert two literal backslashes):

sed '1i\
\\\\' my_text_file

or

sed '1s/^/\\\\\n/' my_text_file

The first one will insert a new line containing two backslashes at the beginning of your file, the second one will substitute the beginning of the first line (^) with two backslashes followed by a \newline (same result).
With osx sed:

sed '1s/^/\\\\\'$'\n/' mytextfile   

You almost had it with:

sed -i '/Hello/{/World/a} appendstring' file

You need to separate your arguments. Use -e, like so:

sed -i -e '/Hello/{/World/a appendstring' -e '}' file

Note that using the append command without a newline is a GNU extension, as is the -i switch.

To do this more portably, and considering as well the possibility of multiple strings to match, try:

sed '/multiple/{/words/{/to/{/match/ s/$/append this/;};};}' file > newfile
mv newfile file

Since you're using GNU Sed already, just use:

sed -i -e '/multiple/{/words/{/to/{/match/ a append this' -e 'a and also this' -e 'a oh and this too' -e '};};}' file