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I thought I had better ride back and comment on your last photo of the manifold, if that is a hole where I have that blue pointer aimed at, then you have big trouble, that part of the exhaust manifold has had it, another reason your engine will be playing up with the exhaust gas heating the inlet manifold, (you can see the black soot mark going up the inlet manifold) this will cause fuel evaporation to a certain degree and make the engine lose power as you commented on in a previous post.
I think you should begin to look for a replacement manifold, you may be able to get the old one repaired, you may be able to do a temporary repair with exhaust manifold gunk, but I can see a repair of the left hand end and the actual exhaust manifold section doesn't look that great overall, sorry for the bad news, something you didn't need to hear right now.
Yes you are correct with your question, the upper section is the inlet manifold where the engine draws in the fuel/air mixture to the cylinders, and the lower manifold is for the exhaust gases to leave the cylinders and be exhausted safely .
Something else to consider with that opening in the exhaust manifold, should the carby leak fuel there with the engine running, then you will have a fire that you most likely will not see if you are using the backhoe until it is too late to fight it, just a thought for you.