No you literally can't use water to heal people unless you are born naturally with that skill. Or at least that's how I interpret the Unique part of that first sentence. It says so directly in the wiki. 
[quote]Waterbenders can sometimes use a unique sub-skill: the ability to heal injuries by redirecting energy paths, or chi, throughout the body, using water as a catalyst. Waterbenders can use their abilities to heal by surrounding a sick or injured person with water, which glows during the process.[4] When infused with spiritual knowledge, a variation of this technique can be used to calm angry spirits, as demonstrated by Unalaq.[49] The use of healing was generally taught to female waterbenders of the Northern Water Tribe, who were not allowed to study combative forms of waterbending prior to the end of the Hundred Year War.[16] Katara is known to be the best healer in the world. With the help of Spirit Oasis water, she was able to heal Aang and resurrect him.[/quote]

Ice is for advanced users of water bending. Katarra only learned it I believe after going to the northern water tribe. True the said can be said of lightning but Ice bending seems like some that would only be useful in the combat area rather than the industrial industry unless it's for cooling areas. Even then that would be just cooling the water in the air not forming ice. Swamp Tribe members have only shown this once or twice in the series from what I read if you insist on being able to use ice I will only allow it if it's very minor and difficult to use. On the other hand plant bending is opened up by having experience in a swamp assuming you can find wet enough objects to use.

Well the swamp tribes would be more likely to become vagrants than northern or southern water tribe members in my own opinion. I didn't say you could not have multiple skins and it's not like it's supposed to be fair.. This city's name is literally earth it's very name should suggest water benders would be at a major disadvantage here. The sewer system may be able to give some water but it will be hard to retrieve and or piping inside buildings could be a possible source of water but again it'd be pretty hard to retrieve without major skill in water bending.