Duchy Of Brunswick 2 Pfennig 1852 - Odd Colour And Weight/Diam Slightly Off

There is certainly a degree of variation in the weight of 19th century coppers. I have no tolerance figures for the Brunswick coinage, but for contemporary French small coppers the allowed tolerance was reduced to 1 % in the mid 19th century, after having been 4 % previously. So the around 2 % deviation from the nominal 4.6 g here is, I would think, within limits.

The colour can vary quite a lot for coppers this old, depending on what they have gone through (this one may have been cleaned at some point). I think the colour of this coin is a normal variation.

I am no expert on contemporary counterfeits, but I think they were more of a problem in the 18th century than in the 19th. My vote is on your coin being genuine.

I have contemporary counterfeits from German States including some with Brunswick in the name.
19th century counterfeits looked better than those from the 18th & 17th centuries. Those centuries were more crude, but especially crude in the letters and numerals. To my eye, just looking at the picture, your coin looks more like a legitimate coin instead of a counterfeit. For what it's worth, I don't recall ever coming across an old German State coin that is the size and weight shown in Numista. As far as color, there is a great variation in what a brass / bronze / copper / billon coin will look like after many years with or without preservation.

Looking at your pictures, I don't see anything out of ordinary with color.
You could check specific gravity to see how close to 8.96 it is.
I don't see any need to do that.
Nothing alarming to me concerning measures.
You could place a certified calibration weight of 4 or 5 grams on your scale to check accuracy.