This sentence is a little confusing because it is itself gramatically wrong in some areas. I will try to address the three bolded verbs:
As a result, **living** in (location) gives benefits to children because the parks offer a safe location for them to play outside
"Living" is a gerund in this case, meaning it is a verb used as a noun. You could replace "living" with "the decision to live" ("the decision" being the noun), or "life". This part of the sentence is fine.
moreover doing lots of outdoor activities
"Moreover" is not necessary here. Also, "doing" is not the correct word choice, although that is subtle. Most importantly, there is no reason for the -ing ending here. If I were writing this sentence, I would say "and participate in lots of outdoor activities" (or "and do lots of outdoor activities", using the verb "do").
assisting them to grow up as health children.
- Health should be "healthy".
- Here, "assisting" is not correct word choice--most native speakers would say "allowing" or "encouraging".
- The reason "assisting" is in the -ing form, is that it is the present participle verb form, and "living" is the subject. Note the difference from the 2nd verb: "children" are the subject of "doing", while "living" is the subject of "assisting".
If I were writing this sentence, I would say:
As a result, living in [location] benefits children because the parks offer a safe place for them to play outside and participate in lots of outdoor activities, allowing them to grow up as healthy children.
I hope this helps. I know that -ing verbs are one of the most confusing parts of English.