There used to be almost no difference between touring and mtb cranks as early mtb's used touring parts and before cassette drives this worked well with freewheels that would have been 13-x while modern mtb cranks are more compact because they can be run with 11-x cassettes and get the same gear range.
An mtb crank with a 24/34/44 mated to a cassette with an 11-30 makes for a wonderful touring set up as you can run a closer spaced rear block and still have decent low gearing and more than enough up top.
Road cranks often use larger bolt circles and will have a big ring of 52 or 53 and newer compact doubles run a lower small chainring to compliment 9 and 10 speed cassettes and offer sufficient climbing gears.
With triples the outer two chain rings are bolted together and the inner ring has a smaller bolt circle to allow for a smaller chain ring... a compact triple will allow for a 20 tooth chain ring and would be used for some rather extreme climbing while most will be limited to 24 or 26 teeth.
Biopace rings can be mixed with round rings... I prefer to use one or the other although a mismatched ring can be used in a pinch.
The square taper bottom bracket was invented by Stronglight and used for many decades and is still a viable system... newer bottom brackets have tried to reduce weight and improve on the bearing quality of the old 3 piece that used cups, 1/4 inch loose balls and races and improve on the interface by making them splined.
Problem with cartridge bottom brackets (most of them) is that they are not as smooth as the old style cup and cone assemblies and despite being virtually maintainence free their performance was lacking... an external bottom bracket addresses this by offering much better bearing support and materials that make for a very stiff and light bottom bracket.