Slightly elongated, slightly flattened ‘S’-Trap
Sneakily hidden, standard ‘S’-Trap
‘Snakes and ladders’-Trap
Is the weir / trap arm not twice the pipe size? Hard to tell from the photo? Don’t know what you guys require up North. 
We require a vented trap same as you guys down South, but then that would be ‘V’ is for … 
So is the weir okay and your just missing a vent? 
Kenneth… off the record and between you and I (as we are in similar areas)…
Pic 1… I would make note of, but not get all worried about it as being a bathroom sink it will never be an issue.
Pic 2… can’t see crap, so no comment.
Pic 3… Yes it has a P-trap, but the real problem is the trap is too deep, and with all that fancy pipery, that thing will constantly clog and back up.
This was my point. Needs a vent. I see so many S traps (this one did not look like one from the pic) in these old homes around here that I don’t and never have gotten worried over them.
Note the increase in pipe diameter after the tailpiece.
“Ain’t nothing to see here”.