VW Golf - killing, restarting rough, leaking oil?

I have an '01 Golf that recently started acting up. When I turn the car after it’s warm (after driving and getting gas) it has a hard time restarting. It will restart, but only after giving it gas. Then it’s super touchy and you have to give it a ton of gas to get out of 1st gear without it killing. This only happens after turning it off and restarting. All other times it starts and runs fine.

Today it’s snowing a TON in MN and we went out to move our cars. As I was pushing my Golf through an intersection and into a spot, my fiance was driving and had the RPMs around 4000. I looked down as the car finally moved and there was a trail of oil and a trail of light green goo that looked, for lack of a better word, like boogers.

The car had a new catalytic converter and two new oxygen sensors about 20,000 miles ago. The ‘check engine’ light has been on, with a code that tells us that either the catalytic converter or oxygen sensors are no good. We took it in and they checked everything and it was fine, so we’ve left it. I have no idea if these are related. We’re snowed in today so we can’t take it anywhere for now but plan to on Monday after the plows come through.

My question is, what’s this most likely to be? Is the leaking oil and green stuff connected to the restarting/stalling problem? It doesn’t leak oil, although it does burn a bit (about a quart between oil changes) and the issues have really only started in the last month or so. Otherwise, it’s always driven very well.