There is so much to unpack here that I don't really know where to start...
Islam in it's first several centuries, with the exception of very early period, expanded almost exclusively by conquest. Initially it did it at the expense of the Byzantium and Persia, but it quickly spread in Africa (East and West Africa - latter called then Western Sudan), rest of Persia and then India. So Europe was but one of several directions of expansion by conquest.
That said, it was a direction that was moved in often - Byzantium was seen as a existential threat to the Ummah, so it was given extra attention, but not the singular, witness the conquest of North Africa, then Spain and following attempted invasion of Gaul. In the meantime, though, there were raids all over the Mediterranean. Battle of Tours was in 732, The Sacking of Rome in 846...
So Muslim conquest was not something Europe was unaware of.. On the contrary, in addition to the actual conquests or raids in force, Europe was subject to constant raiding for slaves for all this time and well into 18th century, with raids known to be reaching British Islands, and possibly even Iceland. (Tom Holland "In the Shadow of the Sword", Christopher Hitchens: Jefferson Versus the Muslim Pirates, City Journal, Spring Issue, 2007)
All the while all that invading and conquering of Europe by Muslim is going on, the trade between the East and West continues more or less uninterrupted. Concept of sanctions or embargo or trade block is pretty recent, back then something so trivial as war was not reason enough for trade to cease.
Somewhat different story is with cultural and scientific exchange. In that period it is, initially, from East to West, simply by necessity - at that period Western Roman Empire doesn't exist anymore, and That part of Europe just begins to pull itself together out of that collapse... Eastern Roman Empire is in decline, mostly due to weakening from recent wars with Persia and successful but costly re-unification of Roman Empires (Italy, parts of Northern Africa), but just militarily and economically. Culturally, almost all the centers are in the East. Islam quickly absorbs those and they, along with the ones established by Islamic states on their own, are for a while, the scientific center of gravity.
But Europe quickly gains and overtakes East in that regard, mostly due to the fact that all over the Muslim world scientific progress is all but eradicated, mostly by the Islamic version of Counter-Reformation, which focuses mainly on the jihad-based concept of expansion and solidification of rule. This all happens in relatively short period of time between 1000AD and 1400AD. (Toby Huff, "The Rise of Early Modern Science")
This caused most, if not all, traces of any potential influence of Crusader West on Islamic world to be eradicated. Not that there was much of that, in the first place.
The First Crusade, while relatively large as a military operation was actually a response to Muslim atrocities happening in the conquered territories (not that it didn't commit atrocities on it's own, of course), and not an effort to stem the expansion of Islam.
As far as Islam is concerned, the Europe was a "al-Harb" territory, so while not conquered it would server as a source of wealth and slaves mostly. It's Cultural achievement were considered irrelevant by Muslims, and of course later were seen as very undesirable. So it can be safe to say that impact of the Crusades on the Muslim society was on the small side, with me personally leaning towards negligible.