Not to solder, but to use a crimped connector - the good ones come with hot-glue-lined heat shrink so you crimp the wires for a great connection, then heat the connector and the shrink glues itself down, making a totally sealed connection.
If it's just low volt, low current, low mechanical stress stuff indoors - just twist and solder and wrap a bit of elec tape around it. But if it matters, break out the crimp tool.
Making a triangle or square or even hexagon with rule and compass is fairly easy. Making a really regular pentagon also only needs rule and compass, but noticeably more knowledge with them. Try it.
That's interesting, I thought the case made for oracular use when I read about it was reasonable, but I may be a bit put of date. There was a fair bit of weird belief washing around in later Roman times before Christianity won out, though.
As for game rules - we have a tiny enough fraction of all non-elite-literary writing from antiquity that we probably wouldn't have a complete game's rules if they had been in the habit of writing them down - but we have so many surviving bits of writing that we ought to have fragments of rules. They seem rather thin on the ground, which leads me to suspect that written rules just didn't seem that important to most Romans. From Vindolanda to Oxyrhynchus they wrote bills and doggerel and love-life complaints and demands for new socks... but nothing at all that attempts to explain THAC0.
We don't even really know how they played Ludus Latrunculorum, despite finding quite a few sets and more boards - but there are several reconstructions from literary references. One of them I find quite engaging, so I hope it's on the right track.
Board games are much older than the Romans, though possibly not older than writing - and texts give us a bit of a clue that some early ones were part recreation part ceremonial. By Roman times pure recreational games were common and reasonably often referenced in their literature. They definitely used cubic dice with numbers on for games (and gambling). The icosahedral dice usually have Greek letters rather than numbers (occasionally symbols IIRC) which make them hard to move a piece to or compare scores; we don't seem to find them with game boards like we do "Latrunculi" counters; there's no textual support for a game with them (weak evidence, true) but there's a fair bit for strong interest in divination and oracles that could use them. So not a dead cert, but fairly likely for the D20s. Whereas when you find a Roman D6, you can be pretty sure it's for gaming and/or betting (or a thief's hit points).
I like that theory too and offer a followon explanation: to make a dodecahedron you must make an accurate regular pentagon and this is not trivial with ancient geometric methods, you need to have learned a thing or two to get there. This makes it a better test than, say, an icosahedron. But we do know that the Roman empire wasn't completely unfamiliar with icosahedral dice, probably for a magical or divinatory purpose rather than determining whether your wizard made her saving throw.
An analogy to this "masterpiece" theory might be the industrial-age "Turner's cube" that demonstrates a pretty solid level of ability with a lathe.
Quite a lot of 25kV AC overhead in the UK. I'm sure it is possible to create a dangerous situation with those and a helium balloon, but it seems to be very rare. I don't think this is a real problem.
There's a similar case in the US - Bridgeman vs Corel - that influenced the UK one. I don't think it forms a universal rule in the US, unlike the more recent UK ruling, but it is influential.