If you have no clearance between the valve tip and the rocker arm when it is cold, don't run the engine until you get this fixed .
When the engine gets to operating temperature, that valve may be open a bit, not a good thing for a valve .
There is oil supplied to the rocker arms when it is running, so oil will drip out of the lower ends .
The oil that lubricates the rocker arms, goes back to the oil sump by way of the push rod tubes, so the rocker box area, does not fill up with oil .
As goergesgiralt said, if a cylinder is cold, it's not firing .
Remove the adjuster that won't adjust properly and post a picture of it, maybe we can see what the problem is .