Have you got it set up as a vst or a stand alone instrument? If its set up properly as a VST then you open up the library and open up the groove you want, minimise your sequencer so you can click on both applications without EZdrummer dissapearing into the background, then click and drag the groove across onto a free midi channel. I'm using Cubase and it works no problem... what version have you got? Also the delay sounds like a latency problem. Seeing as EZDrummer streams from your hard disk it is reasonably ram intensive - how much have you got? Post back if you are unsure how to launch it as a VST.

One of the best pieces of adv ices you can get for getting your system optimised and freeing up resources is to go through all of the tips and tweaks at www.musicxp.net (its recommended by Steinberg - creators of Cubase). Just be sure to open up a notepad file and make a list of all of the changes that you made in case you ever want to go back to the way things were before.