Replacing BB and Chainset only? Presently my bike has an FSA 19mm piece of junk BB and omega chainset. As this is a unique system it has no compatible parts. The bike uses Tiagra 4500 9 speed for the rest of the components. 

If I fit a HTII BB(24MM) and a Sora 9 Speed crankset (50 &amp; 34 tooth like the FSA) will that work or are there any other compatibility issues about not changing the entire set?
Yes, should be fine. Those 19mm BBs are available for replacement though.