Can a 200 amp service split after the main disconnect
Not like that.
Yes but not as pictured. Those terminals are not rated for 2 conductors. Do you have pics of the subpanels?
Yes, but not like that- and none of the 6 load side wires appear to be suitably sized for a 200 amp breaker. Is there a bonding issue also? Looks like the grounded conductors are floating No matter, multiples resasons to just state "Needs immediate attention by a licensed electrician. Multiple wires connected to the 200 amp breaker with undersized conductors noted. The wire installed will not be adequately protected from an overload or overheating as The breaker is unlikely to trip before the wire burns. Recommend review and repair as needed of this panel, breakers, wires and connections by a licensed electrician to assure safe and reliable operation
What Simon said:
That would be the only way to determine if the conductor size is an issue. We all agree that the triple lugging of the terminals is incorrect. Given that corrosion and other issues this thing likely needs to be ripped out and replaced.
Look up NEC tap rules.
Well aware of tap rules. We don’t know how long the conductors are ( the larger ones) smaller look like # 8 which would have additional restrictions. As a home inspector- generalist- not a licensed electrician or engineer, there is more then enough information to defer to A qualified expert for evaluation. Don’t get lost in the weeds
Probably not as likely as a feeder tap as you’ve suggested but it could also be parallel conductors for the larger wires.
I did consider parallel conductors, but I assumed by a split the OP meant multiple remote panels. Where exactly could those parallel conductors go to but a single panel? Maybe he did mean split conductors. Then it could very well be 
Then it would be even more interesting to see how they landed them in that panel.