Change location of zsh’s process substitution ‘=()’

The reason you are seeing the output of the original command is because tee outputs to stdout as well as the files specified. To discard this you can put >/dev/null at the end of the command or redirect this output to one of your process substitutions by adding an extra >, eg:

command | tee >(sed -rn 's/.*foo (bar).*/1/p') > >(awk '{print $3}')

Or simpler just use another pipe:

command | tee >(sed -rn 's/.*foo (bar).*/1/p') | awk '{print $3}'

As for combining the result of the two process substitutions using paste, unless there is some obscure shell trick that I don't know about, there is no way to do this without using a named pipe. Ultimately this is two lines (formatted to more for clarity):

mkfifo /tmp/myfifo
command |
  tee >(sed -rn 's/.*foo (bar).*/1/p' >/tmp/myfifo) |
  awk '{print $3}' |
  paste /tmp/myfifo -

If you are putting this in a script, also consider using the recommendations for creating a temporary named pipe here.

You were really close:

tr "o" "a" < <(echo "Foo")

The substitution <() makes a file descriptor and just pastes the path to the shell. For comprehension just execute:

<(echo blubb)

You will see the error:

-bash: /dev/fd/63: Permission denied

That's why it just pastes /dev/fd/63 into the shell and /dev/fd/63 is not excutable, because it's a simple pipe. In the tr-example above, it's echo "Foo" that writes to the pipe and via input redirection < it's the tr command that reads from the file descriptor.