How long can a colony be shut into the hive? The show is three days long and it will not be safe to have flying bees at the event. Will they be okay for three days? I don't want to show a hive full of bee poo and dead bees by day three!
Observation hives are usually fine for three days, but that does depend on the design and where they spend the night. The at-the-show mandatories are to make sure it's (a) kept out of direct sunlight, (b) insulated at night, (c) adequately ventilated (d) has a source of water so they can keep it cool inside and (e) is checked regularly. You will gradually see corpses and wax fragments being circulated and, with all the frames visible, it will become a bit obvious, but they're usually fine afterwards. Though sometimes they're not.
Five vertical frames is a bit of a stretch, to put it politely, and not just in terms of transport. I'm hoping this is, at worst, two brood frames and three shallows. If it's five deeps, then you'll need to make sure you've plenty of frames of stores at the top, and just one or (if you must) two of actual brood. The bees may otherwise struggle to keep the brood warm overnight (or cool in transit), and with it being spread out more, may just abandon some, or even most, of it. That will not be good.
There will be a feeder (or two feeders) on the hive. If it is hot and there are plenty of stores would it be best to feed them water, syrup or both, giving them the choice?
Water and syrup. Usually an internal feeder holds enough syrup for the duration, while water is trickled through ventilation holes according to need (a bit of a judgement is needed here). Enough so they're not fanning too loudly, not so much that you get excessive condensation or drowning. A mesh floor usually helps with the judging and not drowning aspects (though needs careful checking underneath before it goes in the van). Your design, however, will presumably have a couple of jar-feeders at the bottom, which might be sufficient, provided the journey is very short, the vehicle air-conditioned and you're 100% sure you won't be getting any punctures, traffic jams, accidents etc. on the way.
Would it be best to bleed off the flying bees the day before the show? Would the colony be happier being shut in if they were fewer in number and mostly younger bees? Again assuming there are stores.
It depends how you're running it, and when the show is. The usual pattern with an obs stocked from a hive (or a double-nuc), as opposed to one run as a self-contained nuc, is to stock up in the morning, rather than the day before, and not bother too much about sifting bees (it's finding the queen that's usually the problem), given that a good number of flying bees will be out anyhow.
If it's being run as a colony by itself, you close them up the night before, so the bees that would be flying don't escape, as they won't wait for the show to finish.
It would be nice to use the hive at home to observe the bees and show them to friends. I would like to use a pipe on the entrance so that it is well away from the hive. What is the longest pipe that the bees will be happy with? What diameter should it be?
Length is probably not much of an issue (bees can walk several feet to get to a nest in a roof-space, for example), but short is probably best. There are no hard and fast rules on diameter, provided bees can get through it, but you will probably need to work with what you can get, what will fit on what you've built, what you can easily clean and what you don't want getting into it. From what I've seen, pipes between 2" and 4" inches are popular, but thinner or fatter can both work.
The special issues are angles (flattish will keep the rain out, and downward-sloping will stop rubbish accumulating), corners (preferably none, for the cleaning reason) and joins (you don't want any inaccessible hiding places for rubbish). You also want the bees to have a wide landing patch, so it'll need to be fairly flush to something, or have some sort of structure supporting or attached to it that the bees can land on. It'll also need to keep mice out and wind, which might blow across the pipe, down the pipe or both. Neither is especially good.
That said, set-ups vary, and I've seen one with a five-foot length of vertical drainpipe with a simple cowl on the top. I can't say how well that's doing now. But, if I was going to be spending my time making an observation hive, that's exactly the sort of thing I'd be spending a few years finding out first.
