Surely, you should keep to the right at the lane divider. (You mention some drivers cross to the left: they should not; ignore them.)
Furthermore: in any part of the US I've been in, the implication there is that leaving Lasea you can indeed only turn right. I would consider it "sneaky" to turn left "against" the way they're making you point.
(Sure, as with any traffic regulation, if there's nobody around you might turn left, but IMO the implication is you should only turn right.)
Regarding the people in (1) who are actually driving on the wrong side of the road, into traffic for goodness sake - what can you do? Give them a wide berth.
Google shows that the Stop Sign is "indeterminately" placed sort of in the middle of the lane division.
My interpretation coming to this would be:
"The stop sign is badly placed: bad sign placement does happen. You have to deal with it."
Here's an example of the identical situation, but normally marked....
Leaving a WalMart,
There's a lane divider, as at Lasea.
The stop/yield sign is correctly placed, rather than "sitting strangely in the middle of the lane divider".
You're supposed to only turn right here.
So for me, Lasea is the same as this (fully marked / concreted) WalMart exit: (a) it's ("of course") a road division so keep right; (b) you should really only turn right on to the main road.
Regarding the bizarre stop sign, I'd treat it as a case of "Sometimes signs are strangely placed; that's part of driving."
(For me: the fact that the signage is flakey: I'd go out of my way to stick to the rules even more so - you know?)
BTW I often think when driving ..... this sort of issue will be a real challenge for the "driverless cars" that are coming!