Converting MKV to MP4 Using FFMPEG

ffmpeg -i "$f" -c:v copy -c:a aac -b:a 256k "${f%%mkv}mp4";&& rm "{$f}.mkv"; is a syntax error - you cannot have a && after a ;. It should just be ffmpeg -i "$f" -c:v copy -c:a aac -b:a 256k "${f%%mkv}mp4" && rm "{$f}.mkv";. Then, your $f already ends in .mkv, so the rm command should be just rm "$f".

To recurse into subdirectories, use globstar:

shopt -s  globstar
for f in **/*.mkv; do ... done

All told:

#! /bin/bash
shopt -s  globstar
for f in **/*.mkv
do
  ffmpeg -i "$f" -c:v copy -c:a aac -b:a 256k "${f%%mkv}mp4" &&
    rm "$f"
done

To run it on a schedule, see Running a script everyday using a cronjob or How do I properly install a systemd timer and service?.