Jon

The relative bit is to do with each note being the closest of it's name to the preceding note.
So if the header says

\relative c'

and the first note is d then that d will be the d nearest to c'. The next note will be the nearest version of that note to the preceding d. This is why you don't get capital letters in the same way as you do in ABC.

Relative mode seems to work well with folk tunes.

If the declaration of key is correct I would assume that only accidentals would need to be stated as sharp or flat although that wasn't the case with The Kesh jig.

As to the time signature the capital C after the key signature, three flats, is for 'Common Time' which is another name for 4/4 so the time signature is there.

The beaming in your version is not wrong. Beaming can be forced using [], square braces, but I wouldn't be bothered to try.

All in all that is a pretty good start.

Stan