For sure. Typescript definitely gets you away from the worst of these, the typing mitigates most of the craziness about the two exact issues that you mention. But nonetheless, when the rubber hits the road, it's still JavaScript that is running, so weirdness is definitely still a thing
TS does take into account things like === and you can get warnings for using them wrongly. But I'm not certain... I just don't find myself thinking about === and use strict.
I want fewer broken things to avoid. A subset, not a superset.