MTB, I'm surprised you can't find the info you need on such a well known and well liked aeroplane.
But to answer your questions:
1) In a very general sense anhedral tends to decrease stability in roll, conversely dihedral tends to increase it. A high wing aeroplane (like the BAe 146) tends to have high stability in roll due to the wing configuration, hence the use of anhedral in high wing aircraft (Harrier is another example) to reduce the natural stability to a more acceptable level. The 146 is a delight to fly and displays no vices whatever, which can not be said about more high performance jets like the 737 or scarebus.
2) It is not actually a particularly STOL type.
It does however have the abuility to handle shorter runways than many other jets of comparable size. Why? Thicker wing optimised more towards low speed lift than high speed flight. (Hence it is a short haul aeroplane). Powerful speedbrake allows for steep approaches and deceleration on the runway. Also a very strong and forgiving undercariage that permits positive, accurate and comfortable landings and fearsomely powerful brakes.
3) Cost and complexity I imagine.
4) It is said that there were no suitable engines available at the time of design to make a 2 engine layout but Allison had these tiny jets available and no customers to buy them. = -$$$$$$
The combination of British "short termism" and the desire to take advantage of a "cheap" option regardless of long-term cost to the entire project served to condemn this otherwise world beating design into one that only enjoyed moderate success.
5) Odd situation that is well known and well publicised re operation of engines in icing conditions above FL260. Regrettable but to be fair one that only became aparrent years after introduction into service, and even then only in the most peculiar and unusual weather conditions.
Before you get any more info you'll need to reassure us that your're not a journo trawling for (non-existant) dirt on this fine type of aeroplane, an impression that is amply given by the nature of your post.