…from a beginner who does not yet have his first flute in hand.
What is the foot joint/extension/thingy for? Many of them have two holes, which appear unreachable. What is the function?
Mainly due to imitation of the original flutes’ design, which had been designed to have keys there for C# and C. Some flutes can be retrofitted with those keys. Others cannot and the C foot joints are for decoration mostly. Some people say it makes the flute feel more balanced.
Whether or not the flute can be retrofitted with keys, the first open hole will be the hole which gives you the flute’s bell note (d in the case of simple flutes normally). Plugging them with anything isn’t a good idea, either. 
Yup, exactly. I took delivery of a Delrin flute recently, and although I have many good things to say about it, the one thing I wish it had is one of those foot joint things, the one with the extra holes in it, just to better balance the flute.
It’s not bad the way it is, but that little bit of extra weight would be just right.
Interesting. Vestigial tone holes. Or you could get a friend to stand next to you for that occasional C and C#. A very quick and dexterous friend.
i actually know someone who did that once on an album recording!
On some flutes the non-fingered vent hole on the end of the flute (bottomside) can be covered by holding the flute against your leg.
Casey Burns expained recently that the redesign of his folk flute into more than two pieces was prompted by two factors: 1) it is easier to find smaller pieces of wood that are suitable for making flute bodies; 2) it is easier to machine the internal taper (conical bore) of shorter pieces of wood, hence 3 and 4 piece flutes.
As has been mentioned, wood flutes with metal-lined headjoint and metal tuning slides are often head-heavy unless the flute body can be long enough so that the head doesn’t fall away from your lips while you are holding it. The only way that you can have a longer flute is to use non-fingered vent holes (or open holes with keys) near the end of the flute.
What’s interesting is that the Bulgarian kaval, an endblown wooden flute often in the same key as Irish flutes, also has these two holes, and evidently always has had these two holes, though these never had keys on them. Besides those two holes there are two more holes further down on the kaval footjoint, these two at the same position along the bore and directly across from each other, just like the ventholes on a Highland bagpipe chanter.
Many “folk” instruments have these ventholes.
It’s interesting that the “Irish flute” should by a completely different route aquire a common folk instrument feature.
I actually had a Casey Burns flute years ago that he sent with two footjoints, one short and the other long with the two ventholes. I couldn’t really tell much difference. Perhaps the bottom D was a tad stronger on the short foot. Supposedly the 2nd register is better with the long foot but I couldn’t detect a difference.
By the way, an Irish fluteplayer I knew, when asked about those two ventholes on his flute’s footjoint, would reply, “de Devil plays dem holes”.
Although the three pedals on the piano are not vestigial, many students don’t know what the left two are for (the right is, of course, the damper).
So I tell them the right pedal is the gas, the middle is the brake, and the left is the clutch.
Interesting. I think I had read here that one of the reasons for the vented footjoint was to produce better evenness of the D note(s?) with the rest of the scale (venting with a tone hole as opposed to an end hole).
Re: pedals etc. - of course, the faster you pedal, the faster you go! (Except on a Harmonium!)
Precisely. The brake is for rests, fermatas, ritardandi…
The clutch is, I suppose, for indecision and memory mistakes.
Ahhh, has it a straw linkage? (Dare I say, for those with feet of clay???)
Then of course, there’s always the “little old man on a bike syndrome” - i.e. “if he goes any slower he’ll fall off!”
Then you really need to install a faux-gearshift lever. Run up through the gears for those accelerando passages, first for adagio, top gear overdrive for presto. I’m not sure how you’d explain reverse!
And shifting and playing at the same time is a very advanced technique. 
Interestingly, Ken Matsusaka at SZBE also makes whistles with an extended foot joint. Inspired by European or Asian flute design, or maybe both. I have a custom convertible model similar to this one, and notice little difference in bell note or intonation with the short or long joints. And on a whistle, I find the long joint unbalances it, but it’s a real conversation piece. A very nice whistle in either case.