Byzantine Empire expands overseas

It depends on what you define as "technology" in the early Renaissance / late Byzantine period.  The Byzantine emigres brough priceless manuscripts and the ability to read and copy them with them to Western Europe.  Western scholars received Greek literature that had been unavailable to them for centuries.  Among these works were ancient mathematical treatises and studies from Aristotle, Ptolemy, Pythagoras, and others.  The Byzantine teacher Manuel Chrysoloras was a mathematician and taught the subject in Italy.  Many of the Byzantine scholars were interested in philosophy (Neoplatonism and Aristotelian) and the humanities (non-scientific literature).

If the later Byzantines had made any technological advances or scientific discoveries, you would think that they would have had the sense to put these advances to good use.  I guess, due to the lack of resources to fund research and the implementation of advances, nothing really happened.  On the other hand, in the typically Byzantine tradition, scholars of the late period were more interested in theology and philosophy - see Gregory Palamas and Gemistus Plethon among others.  Great advances, or highly stylized writings, were made in these fields as the physical world of the Byzantines crumbled. 

I have always thought that the later emperors would have imported Italian knowledge of fortification building and the science of gunpowder weapons to help them in their struggle against the Ottomans.  The old Theodosian Walls could have been improved with angled bastions and artillery towers.  Nevertheless, this did not happen.  Although there is some mention of the Byzantines using cannon in the last two sieges of Constantinople (1422 and 1453), there was no actual cannon foundry in the city until after the Ottoman conquest.

Yes, you are exactly right.

As I said, the extreme lack of resources that the later emperors were faced nixed any attempt they could have made to develop new technology or import the knowledge and the technicians from elsewhere.  What few gunpowder weapons they did have most likely came from either Hungary or the Balkans.  Urban the gun engineer illustrates this; he was most likely a Hungarian Christian.

They did not abandoned it, they were pushed out due to the integral deficiencies of the Byzantine Empire, which was fast to exchange its long-term prosperity for near-term benefits. E.g. they would buy from the Venetians a service (e.g. to land a force at some Dalmatian coast or to attack a city) and pay with e.g. tax-free commerce in the ports of eastern Aegean. That became a practice that was expanded to the Genovese and other Italians and led to the destruction of the local merchants and shipowners to the benefit of the Italians and mainly the Venetians & Genovese.

 The fighting ability of the Catalans is something I certainly wont dispute, they appear to have been thoroughly brilliant soldiers, so few in number aswell which makes many of their victories even greater.

 The assassination of Roger de flor was obviously going to enrage the Catalans, but they were mercenaries how long where they going to play to the empires tune before looking to their own interests? They must have seen an opportunity to create a small Catalan empire in Asia Minor, the last thing Byzantium needed was another potential enemy.

 I'm wondering though, how would anybody else have dealt with the Catalan problem? you cant get rid of them through force, you cant buy them off because your pretty much bankrupt by now and cant just hope the problem goes away these guys want paid and terirtory of their own.

 If the Catalans could be controlled theyd of been indespensible, I cant help but think if only theyd been around a century or so earlier.