With 'dort' replaced by 'da' how does the meaning change for this sentence?
"da" is closer than "dort", and can mean "right here". So... probably like saying "His profile is over there" versus "His profile is there".
When you say "da" than it can also mean that something is existing and close by. You can also use it, when someone or something has arrived like "Er ist da" = "He is here". I hope this makes sense
What does "Profil" mean, exactly, in this sentence?
That would depend on the context of the rest of the discussion. I just assumed it's something like his Facebook profile or criminal dossier or whatever.
Why not in singular? Like "His profile is there"
Because "Profile" and "sind" are both plural.
Usually a person only has one profile.
Not necessarily. I might have one profile on Facebook, for example; a slightly different profile on LinkedIn; yet another on a group about native plants; adjusted according to what is pertinent for each context.