You cant delete explorer because its part of windows, so just leave it on there and carry on using firefox for your browser.

You say "it came up"? i assume you mean the same pop up you were getting on explorer? if so then can you post a screen shot on here of it so i can see for myself?

As for the cookie tracker, you will get them from visting different sites, basically some websites attach these tracking cookies so they can moniter your internet usage habits etc and find out things about you etc! i always have at least 6 of these when i do a scan so i just delete them and thats it, nothing much to worry about.

P.s when you have done a scan using ad-adware if you right click on the cookie thing it will say something like"whats this", or "definition"(i cant remember) and it tells you exactly what the item is that its found