Oh, that's a good translation, quite understandable for those who don't know English at all...
But there are some uncouth places:
S1L1 каждый вид красоты - > normally we don't say like that in Russian. Sometimes we say "красота какого-либо рода" but a collocation like "род красоты" is still somewhat out of the way in Russian, though it's fully understandable. You may use "тип красоты" instead, that is much more comfortable. "Проявление красоты" is another possible variant here. :)
So, I'd translate this line something like this: Она - любой тип красоты, каждый - по-своему
S1L2 написана внутри->записанная внутри (that sounds better in Russian, though the meaning is the very same) :)
S1L3 глубоких мыслей->сокровенных мыслей (when a Russian reads "о глубоких мыслях" he will start to think "глубокомысленно", and that's not a good moment to do so) ;)
S2L1 любое бескорыстное дело->нечто, делаемое бескорыстно (that better corresponds with the continuation of the line containing a participle)
S2L3 видимое does not give the intended meaning here. It'd be better to change it into "открытое", "явное", or even "открыто демонстрируемое"
S2L4 нам удается завершить ->мы [в известной мере] совершаем (you can safely omit the phrase in brackets because it (or any of such parenthetic words ever) is not likely to be said when speaking in Russian)
S3L2 мы себя с собой хорошо чувствуем-> that's too redundant in Russian. ;) There's one good way to translate this expression into Russian: "у нас всё хорошо", though it may have another possible idiomatic translation like "мы в ладу с собой".
S3L3 в нашей души->в нашей душе (a minor typo, I suppose) :)
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