As far as Italy is concerned, no - not least because the Muslim presence was largely limited to the island of Sicily, while the few bridgeheads they'd gotten on the southern part of the peninsula's heel didn't last long and were wiped out.

Moorish rule in Sicily actually lasted a bit longer - little more than a century - but that one too had ceased to exist by 1091, as the place had fallen to the Normans... a few years before the Crusades had even begun. I'd argue that this, coupled with the fact that the Muslim holdings in the Iberian peninsula were far more important (and lasting) than those in Sicily, might have something to do with the lack of efforts aimed at an eventual reconquista of the island.

Please keep in mind that I'm not a professional historian - I'd wait for other answers.

Yes, in the case of Spain they did, repeatedly. Sincé the fall of the Umayyad caliphate in the XI century, several muslims empires rose in north Africa and they all invaded Spain reuniting the different spanish muslim states (the Taifas) and fighting agains the Christian ones. Main examples are the Almoravids (XII century), the Almohads (XIII century) and the Benimerins (XIV century).