I can see most of this answered, already, but putting my oar in anyway.
I've seen people being misled by the "No suitable soil, create mud with water"-like message, which appears. That message might well appear because your above-ground biome (e.g. one where it's glacial) doesn't allow
any plants. If you have soil, you don't need irrigation at all, and can build a farm there. If you then can't grow anything, you either don't have any suitable seeds at the moment (aboveground for lit, even recovered, tiles, subterranean for any never-exposed-to-sky) or, aboveground only, the biome doesn't want you to plant at all and it'll
never work
However, if you're wanting to plant on bare rock, as opposed to dug-out soil, you would need to irrigate. As has been said, only existing pools can refill with water when it rains. You need to tap into one of those. When I've done this (on particularly dry biomes, and back when
even soil needed irrigating, underground) I've tended to set up a floodgate to allow a pool to fill an underground cistern twice its size (could be bigger, but hedging against evaporation of the leading edge of the waters) on the level below. That cistern has a floodgate leading to one twice
its size, to be emptied into once two or more surface fillings have filled the first cistern, and I might chain a few more double-the-size cisterns, emptying each into the next when full, in something like a binary-carry cascade.
These days, however, I'd tap into cavern water. You'll almost certainly find some that connects to the edge and is infinite, and even if it isn't you should be able to tap into it for a significant amount of water, if you design the collection system correctly.
The slower way to tap into it is to make a well-head, and use that water-source to manually ('bucket-brigade') fill a pool of your designation. I'd make it a 1x1 pool connected by a floodgate to a second 1x1. Very quickly there'd be greater than 1/7ths filled, and when it's 7/7ths, opening the floodgate would make it 2+2+3/7ths (perhaps 2+2+2 if there's a small evaporation) filled between the three rooms. Which can then be filled back to 7/7ths via the original opening, and then you can open up a further floodgate to let the 21/7ths spread into half a dozen other tiles (including/plus second floodgate space) without overly evaporating, and so on. This way you can accumulate a separate cistern supply. Designing the well/well-head so that it can be shut off and prevent flying cavern beasties wandering in might be important.
The quicker way (has some danger, but less labour intensive, once dug out/constructed, and easy to replenish) is to dig into the side of the body of water. Set a tunnel almost to the end, set so that a final (undug) tile would give a diagonal connection between tunnel and/or flooded area. Smooth that tile. Construct (and level link) a floodgate in the penultimate (current end-of-tunnel) tile. Set it to be opened and the final tile designated to become fortification-carved. When the engraver completes the job. the water will rush in but you
will have ensured that he's got a quick exit (
not via an entrance on the same level, but up and out of the water-duct, but up a level), as well as get the floodgate closed again, quickly. When all is well, engraver is out (or, if you still messed up, body and possessions recovered and dealt with) you can seal/unseal this water-pipe as it enters various other places, equip more floodgates, grates, grills, whatever, and when you're happy open the floodgate back up again to gain the water supply you need.
For safety, unless you're absolutely needing a continuous water-supply, I'd close the floodgate
again once it's purpose is complete (trapping mostly 7/7ths water in the tunnel, which you can still use for safer well-abstraction, etc, at least until it's plundered a while) preventing anything squeezing into the tunnel (or bodily-fluid pollutions of any kind) that might cause you grief.
But back to your numbered questions:
- I would designate to dig a channel on one tile (1x1) across a vertical column (i.e. 1x1 on a given Z-level, the same point 1x1 on the Z-level below, etc). Make sure you don't drop into any voids, and that you have (or can dig) an exit tunnel off to the side at the final layer. The miner will channel at the top level, go into the channel to channel in the layer below, and from then until he hits bottom (or is otherwise rescued/recovered, if you encounter a problem you didn't foresee) he's trapped and will dedicate himself to digging out into the next layer down. Then either dig or walk his way away from the bottom end, according to whether you got him, or another guy, to pre-dig the exit route.
- You can apparently cave-in layers (undug ones), to this effect, but it's a messy, dusty business. Might not be for beginners.
- Already answered, grass(/moss) and other subterranean plants will grow once you hit caverns. It's not quick, but it's certain.
- I just (d)esignate a normally (d)ug sideways mining tunnel, and rarely cut'n'cover, and only ever need walls/floor built if I've hit a void that I don't want or I've removed valuable ores from the tunnel walls.
- (b)uild and (c)onstruct a (f)loor on that spot.