Actually it's the other way round. CaCO3 is more soluble in cold water than hot but it is not, in either case, very soluble.
Also sort of the other way round with calcium hydroxide. It should be treated with respect, of course, and has the same health rating (3 - "Short exposure could cause serious temporary or moderate residual injury") in the NFPA diamond) but it is much less reactive than quick lime which releases tremendous amounts of heat when exposed to water to the point that fires have been started by it. Don't get either form in your eyes, of course, but skin contact with slaked lime is not likely to cause much of a problem. After all, the stuff is sold in super markets for use in making pickles.
Concentrated sulfuric acid is, IMO, much more dangerous than slaked lime though it gets the same rating, 3, as slaked lime. It will tear the water out of anything thus causing nasty burns if it touches your skin (and certainly eyes).
But I don't think this is what you are asking. You have observed that natural water, which contains a lot if calcium bicarbonate, is produced by the action of carbon dioxide on limestone over long periods of time and, I believe, want to know how we would produce this in the brewery on a much shorter time scale. The answer is that in the vast majority of cases we don't because we usually want to get rid of bicarbonate. If we strive to produce carbonaceous water to mimic, say, Munich's, we would then presumably want to treat that water in the same way a Munich brewer does, i.e. decarbonate it, before brewing. If we are going to take the bicarbonate out as the first step in brewing why bother to put it in in the first place?
If we do want to make carbonaceous water for whatever reason and we want to do it quickly the only reasonable approach is to do exactly what nature did but to do it under relatively high CO2 pressure in order to speed the reaction. Thus we'd put chalk (finely powdered limestone) into a Cornelius keg (or similar vessel which can be pressurized, fill with RO water, seal, pressurize and agitate. The CO2 will dissolve turning into carbonic acid which will in turn dissolve the chalk. Control of the process is a little tricky as for a given alkalinity you must hit a particular pH. This is probably most easily done by dissolving enough CO2 (the amount required will depend on how much chalk you put into the keg) to get the pH well below what you want and then letting CO2 escape on standing after removal from the keg until the desired pH is reached. You can calculate the amount of chalk to use but it's a little tricky to do so. The math is in the Sticky here on carbonates and bicarbonates. Nature can help you with this. Upon standing for a good while (we're still slaves to time to some extent here) the water will come to equilibriun with the CO2 in the air and will have pH around 8.4 with alkalinity and hardness of about 1 mEq/L.
