How to echo out things without a newline?

Yes. Use the -n option:

echo -n "$x"

From help echo:

-n do not append a newline

This would strips off the last newline too, so if you want you can add a final newline after the loop:

for ...; do ...; done; echo

---

Note:

This is not portable among various implementations of echo builtin/external executable. The portable way would be to use printf instead:

printf '%s' "$x"

printf '%s\n' "${array[@]}" | sort | tr '\n' ' '

printf '%s\n' -- more robust than echo and you want the newlines here for sort's sake "${array[@]}" -- quotes unnecessary for your particular array, but good practice as you don't generally want word-spliting and glob expansions there

You don't need a for loop to sort numbers from an array.

Use process substitution like this:

sort <(printf "%s\n" "${array[@]}")

To remove new lines use:

sort <(printf "%s\n" "${array[@]}") | tr '\n' ' '