Q1. Here, just like means it is just like. It's referring to whatever was in the sentence before.
For example, I might say:
Fred was moaning about his job again, but he never bothers to look for a new one. It's just like Teresa's complaining about the landlord: if it's a problem, do something about it!
The just like is comparing the two situations - although they are different situations, the writer is drawing a comparison because (in this case) both people are complaining about something they can change, but they're not making any of those possible changes.
In your sentence you could lengthen it to
It's just like how everyone has their own features but they are nearly the same.
It's just like the way that everyone has their own features but they are nearly the same.
Q2. the same here is idiomatic usage: it's the phrase the same as. The longer version would be:
Everyone has their own features, but they are nearly the same as each other.
Edit: @Maulik makes a good point about the same: it takes the definite article because it is referring to a definite thing. You have to be talking about something specific in order to be saying it's the same as something else.