The objects aren't aligning accurately to the artboard.

If you're seeing this outline offset glitch at 46000% zoom the objects in your example images must be really small. I've tried to re-create the issue on my system using similar tiny objects at maximum zoom level. I can see a bit of misalignment between the object's fill and the blue selection highlight outline. The offset is more visible in GPU Preview than CPU Preview. The misalignment doesn't seem as bad as it appears in your examples. I uploaded a screen shot of what I'm seeing on my end.

If the objects are sized normally there is very little if any misalignment between the object's fill and the blue outline highlighting the object selection.

Regarding issues of white borders contaminating the edge detail of exported graphics: that will always happen if the object's edges aren't sized/aligned with the pixel grid of the exported object's target size/resolution. If the edges are lined up partially over the next pixel in the grid the edges will be fuzzy.

JPEG isn't a good format to use for exporting web-friendly versions of graphical items. PNG is far better. PNG will keep flat areas of color uniform looking. JPEG will introduce varying amounts of noise and macro-blocking into flat color areas, depending on how severe the data compression level may be. PNG also supports transparency. Any object edges that are fuzzy will look slightly less fuzzy in PNG format than JPEG. Still, it makes a difference to size/position vector artwork as "pixel perfect" as possible if it will be exported in PNG or JPEG formats.