The Al-Aqsa Intifadah (which began, I believe, in about 2000 when the Camp David talks were then stalling) was begun by PLO and still exists today (much less actively than from about 2000 to about 2004, roughly) under the PLO umbrella. 3) Democratic nations including Great Britain and the United States have long called for democratic elections in Palestine. Now that Hamas was the unexpected winner of the first elections, should it be recognized by the United States?

No; at least not officially, since Hamas has been from its 1987 outset, and clearly is today, an overtly, aggressively and ruthlessly terrorist organization recognized internationally as such. Still, Hamas should definitely be talked to by the United States, as horrendous a prospect as that might well seem (and is). And unfortunately, it has become almost risible in today's world that Great Britain or the United States could still even semi-seriously think Palestinians care what sort of elections they would prefer to see there. This is the West's blind spot.

Hamas's longstanding complaints against extreme Israeli aggression against Palestine should also be seriously listened to; and Israel should cease with its brutality. American (and Israeli) bullying of Arab or other Islamic states and nations has not and will not win friends; but I can think of no foreign situation, now or in the past, in which dialogue, rather invited or accepted by America, ever did harm. Hamas is convinced Israel (and by association the United States, which supports Israel) are evil infidel invaders of Palestinian territory; and in the strict Islamic sense (i.e., of encroaching physically on Palestinian territory) Hamas is right.

Under George W. Bush especially (e.g., one might consider the President's recent refusal to talk to Syria), the United States has developed, especially in recent years, the bad habit of disregarding the ancient Chinese general Sun Yat Sen's timeless advice within his military classic the Art of War: "Keep your friends...

And the European Union? Explain your position and support it using what you have learned from the unit resources.
I think that African terrorist hubs in particular (including but not limited to Al Qaeda ones); if not so much the small home-grown terrorist cells within sub-Saharan African states whose governments have failed, do indeed pose a current and/or future threat to American and European Union interests, especially n places like Somalia; Sierra Leone; and Liberia. Terrorist hubs in those nations, in particular, are probably (in my own opinion) substantially more dangerous to America and Europe than are the small home-grown terrorist cells within such nations; this is because terrorist hubs (anywhere) are by nature international gathering spots. Obviously, Al Qaeda hubs in particular are always a threat, and should be treated as such by the U.S. And E.U., wherever they happen to be.

Presently Al Qaeda cells in Sierra Leone reportedly profit handsomely (thereby potentially becoming greater and greater threats to the West) from members' working inside the enormously lucrative underground diamond trade in that nation. I have also read various reports in newspapers including the Wall Street Journal and Ha'aretz (I subscribe to both online) of Al Qaeda money-laundering in Somalia and possibly also in Sierra Leone and Liberia. Al Qaeda reportedly also sponsors terrorist activity throughout Eastern Africa, including the building of new and the strengthening of existing terrorist hubs. Unfortunately, hubs all-too-often operate undetected by Western governments, for protracted periods, while being lucratively-involved in sub-rosa endeavors like illegal arms sales; money laundering, etc. So to still not consider African-based terrorists a serious threat and potentially very serious danger to the West is foolhardy.