Hello @leftyuk  I'm far from being an expert on playing celtic music -- or any other music for that matter, but here are some things that might help. 

First, one of the most respected Irish fiddlers, Kevin Burke said:  There are bowing rules for Irish music, but I don't know what they are. 

You asked if there was a rule of thumb for where on the bow to play.  The answer to this question is yes -- the middle of the bow is where you'll find yourself most of the time.  Because there are so many rapid string crossings, being near the fulcrum point of the bow is a distinct advantage. 

To learn to play trad Irish music, really learn to understand the rhythms of Irish music.  There are many different types of rhythms and they each have very distinct accent patterns, including  double jigs (6/8), hornpipes and reels (4/4), slip jigs (9/8) and single jigs (12/8), not to mention polkas, aires, barn dances, slides, hop jigs, marches and a number of others.  Keep in mind, that almost all Irish music is written for dancing and not for the sots at the bar sipping a pint. As such, the beat is of paramount importance. Once you have the beat, the bowing will happen more or less naturally. 

This might help with a couple of other tips:

OK.  I kind of see your problem -- I think.  As far as the bowing goes the pickup notes start (generally) on an up bow so that you start the first measure on a down bow. It's 4/4 time so it's pretty much down, up, down up all the way though, using the middle of the bow.

I don't think it's the bowing that's actually your problem, but the notation and the rhythm.  Dotted hornpipe's are notated this way, but it is not an accurate depiction of the rhythm.  Hornpipe's are played with what is called a "swing" rhythm.  That is that some notes are played for longer than their notated value and some notes are played shorter than their notated value. This dotted notation is there to give players and "idea" of the rhythm, but it's not the "actual "rhythm and will always sound a little "off" if played the way it is written.  

A dotted 1/8th note (3/16) plus a 16th note (1/6) is a 3 to 1 ratio.  The actual swing of a hornpipe is closer to 2 and a tiny bit to 1. The actual playing of "dotted" hornpipes is much closer to the way they would be played if written in 12/8 time with quarter notes and eight notes which gives a 2 to 1 ratio.  If someone did that and called it a hornpipe though, the notation police would come and arrest them at once -- but it's closer to the correct way of playing it. 

Often they are just written as eighth notes and it's assumed that they player knows to swing the beat. That's the thing about playing ethnic music, it often doesn't lend itself exactly to traditional notation. 

Your best bet is to just listen to a lot of hornpipes and tap your foot and/or clap your hands to the rhythm until you can feel it.  You'll notice that you're not clapping a regular rhythm like a metronome.  It's more like french fry, french fry, french fry, or tune it, tune it, tune it... Then play the tune to that rhythm, realizing that the notation isn't literal.