Actually, there is no definite way of "parsing" a sentence, i.e. distinguishing the components : it depends on the context. See for example this very funny twitter thread about the sentence, where native speakers try to find all possible interpretations :
頭{あたま}が赤｛あか｝い魚｛さかな｝を食｛た｝べた猫｛ねこ｝
However, it should be obvious that in a given context, only one sentence is acceptable. In your example, the first thing to notice is that 「写真があった」 is a proposition that modifies the noun following it, i.e. 方.
People who have a (profile) picture.
The next が shows that 方 is in turn subject of the next clause. The next verb being わかる, we need to find the function of 「あなたがどんな人なのか」. Well, this would be the object of わかる. It is an indirect or embedded question : meaning that people will understand the answer to the question 「あなたがどんあひとなの」.
This sentence ends with 「し」, here showing a reason among others. Thus :
One reason that it becomes easy to make friends 「フレンドを作りやすくなります」, is that people can understand what kind of person you are if you have a profile picture.
This is obviously subject to interpretation, and we lack context but in this case, I do not see any other way of splitting the sentence in parts that make sense.
「写真があった方」が「あなたがどんな人なのか」わかるし、フレンドも作りやすくなります。
My guess would be that people who see your profile picture would get a better understanding as of who you are !
And no, I do not see another "less confusing" way of writing this sentence. It is true that it contains nested propositions, but this is very common in Japanese.
