Its an old-style white handle screw-in primer pump. I ordered a new Bosch black primer pump today. Couldn't get one locally - from anywhere, including the dealers in the area. Hope it arrives by Friday.

If I can figure out what diameters the fuel lines are I will try to buy some replacement hoses at a local Napa or Advanced Auto and switch out the old hoses before the primer pump arrives. I assume the manual will tell me, but if not where else might I find this info? I did a search on this forum but didn't see any posts for an old 220D.

I'm not sure how much blowback I'm gettting. If I unscrew the oil cap and just have it sitting on the fill hole while the engine runs it does not jump around or anything. But when I remove it specks / drops of oil do come straight up and out.

I'll start researching how to adjust the valves once I get the fuel / pump issue worked out and the car actually runs again!

so you do have some blowback,so your rings may be a bit worn, valve seats can contribute
the valves are done cold so when an engine is not running is a good time to do them:D
Yes get rid of the primer pump, most MB shops have the mm tubing you need and sold by the meter, get the right stuff, trying to clamp oversize is a pain in the patutie