That breather hose from the valve cover goes into a recirculation system connected to the intake, on a 16V anyway. If it wasn't blowing smoke I'd say cap it with a filter and call it good, but the fact that it's smoking IS a good indication all's not perfect in your top end and to keep all that oily soot and smoke out of the atmosphere and your lungs, I'd say reconnect it. Look for a male fitting on the intake manifold or intake tube from the airbox. Check your PCV too, it may be a bit plugged up.
The EGR passage (through the head) can be cleaned with a stiff wire and solvent. It will get clogged if your engine isn't in the best state of tune, but it's not uncommon. Lots of threads about it.
The disconnected breather may be the cause of some of the condensation in your engine, especially if it's been paticularly wet or damp where you are. Or it just may be another issue althgether. Is there any other smoke visible out of the exhaust? What you may be seeing is the moisture burning off. Or a bad ring or valve guide. Does it smoke all the time?
If you tend to drive short distances more than long, it's not unusual to get that kind of condensation in your engine too, just take a look at the water squirting out of tailpipes on many cars. Most drivers never get there engines up to temp for very long, just long enough to get the condensation started but not long enough to stay hot enough to burn it off. 25 miles on the freeway should do it. I've seen engines with only 60/70 k on them ready for valve jobs because they never got drivin hard or long enough.