I have been wanting to learn archery, but sadly don't have the funds for that at all... It'd be fun, but it's been well acknowledged that chainmail isn't even designed to handle arrows. If anything, arrows are designed specifically to pierce chainmail, so that's not a fair test at all. Besides, you can look up dozens of youtube videos of chainmail getting shot. Usually, chainmail stretched taunt over a hard surface being shot with bodkin/broadhead arrows at 10 feet from a compound bow...
I managed to get into archery for about $200. Bought some wooden longbow off the internet for about $100, a couple dozen arrows, a quiver, a bracer and finger tabs for the other $100. That's not so bad, but it's hardly historically accurate, and those are practice tips and not anything like a war arrow.
Of course, I wouldn't say that I've actually learned archery from it. I just mostly looked up how you're supposed to pull the string and then started shooting at bits of styrofoam I braced around in my back yard. I'm still an absolutely awful shot after even about a year of practicing off and on.
Anyway, I'm pretty interested in this thread too. I started making some chain mail some time ago but never made very much because I got distracted by trying and failing to learn to make plate armor.
I suspect that butted mail won't stand up too well to being whacked with the axe, at least on a plyable surface, but I'm quite curious to see how it works out regardless. A 6-in-1 weave might actually repel arrows surprisingly well, I'd be interested in seeing that. And above all else, if you do end up making some titanium chain mail, I'd love to see if it stands up to the abuse better than steel. I've read in a number of places that pure titanium wasn't a particularly good material for this, but I'm not sure why. Apparenty it's a royal pain to work with, if nothing else.