My cursory research on the second question indicated that the US wasn't involved in battles in Europe until 1943, but I couldn't find anything on if there was an American presence prior to that; specifically I'd like to know if there were American troops present in Europe on October 31st 1942.
And how would someone find out their brother was MIA? Would it be in-person? A letter? A phone call?
How long would it take for the military to officially declare a soldier MIA, and how long between that decision and the family being notified?
(I hope that this sort of two-questions-in-one isn't a problem? I've never posted here before and as far as I could see there isn't anything in the rules against it.)
As for your question regarding American troops in Europe prior to 1943: Yes!
Among the first US soldiers actually fighting in Europe during WW2 were a detachment of 50 US Army Rangers taking part in the Dieppe raid (Operation Jubilee) operating alongside British Commandos. The raid took place on the 19th August 1942 and the Commandos (including Rangers) operated on the flanks, intending to take out the coastal artillery prior to the main landning.
Edwin Loustalot, charging an enemy machinegun, was the first US infantry officer to be killed by enemy action in Europe (see Terence Robertson's Dieppe – The Shame and the Glory, p. 223). Note that Robertson specifically mentions him as an officer casualty, implying there might have OR ("other (lower) ranks") deaths before him.