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Hello!

I hope somebody on here could help me out with this, as I have been to some mechanics and nobody was able to tell me anything about it.
My EK3 Honda Civic runs great, healthy engine, very nice idle (except one thing I will get to later).
I noticed when there is little load on the engine and I press the accelerator hard and slightly let go, the car shakes violently back and forth.
This is especially apparent in 1st and 2nd gear when going at slower speeds.
I really wonder what this could be. Spark plugs are new, timing is set with new belt, I doubt its a slipping clutch as that (I think) would feel different.
Another thing I noticed is that on a cold engine, when I rev it up, is that the revs first drop normally but then move up about 200-400rpm for like 2-5 seconds, then return back to normal idle, which made me think along the lines of Vac-leak, but I am not sure how to test that further.
Is there any easy diagnostics that I can do? Parts I can replace that arent too costly simply in order to look for improvement?
Any pointers in any direction are very welcome.

Another thing, maybe related to the problem at hand or not:
- The images I have provided show the engine bay, where I found that one certain hose is not connected to what seems like a black circular component mounted to the firewall.
The hose itself looks kind of rough and I wonder if it is a problem that it is not connected.
- Also, there is some strange electrical wiring coming of the MAP sensor, I wonder if that looks normal or not.