double wired circuits and grounds and neutrals sharing the same bus bar. Is it OK?
No on several counts.  

This looks like a subpanel.  Neutral bars and ground bars must be rigidly separated in subpanels. Period. If there is groundless feeder coming to it, you still need to separate neutrals and grounds for that happy day when you retrofit ground, which is legal anytime. (well, since 2014 for almost all circuits). 



Note how the main lugs are double-tapped.  You cannot do that unless the lugs or the equipment they come with says in the labeling or instructions that you can do that.  Because the UL listing depends on following the instructions. 

To fix that, see if the lugs are replaceable.  If they are, see if they can be changed to duplex lugs (lugs with 2 voids).   If they can't, then get a 3-hole Polaris connector and a short pigtail for each hot.  

Often the small holes in the neutral or ground bar can accept up to a #6, and often those bars have some holes intended for larger wires.  Using those is fine. 

Another way to avoid double-tapping on that panel is to move one pair of wires over to a circuit breaker of appropriate size. That's  a $10 solution.  This can double as a subpanel breaker (if needed) or outbuilding shutoff switch (if needed).  For what it's worth, they do make double-stuff breakers in CH. 



Speaking of that, you cannot double-tap the neutral bar (2 neutrals on one lug) again unless the labeling or instructions say you can. 

Ditto ditto grounds, though I have heard of panels saying you can up to triple-tap a ground lug.