The extractor slips over the rim of the cartridge and is what allows the bolt to withdraw the fired brass from the chamber. As long as you can reliably extract the fired case from the chamber, this isn't the problem.
The ejector, in the case of a push feed, is a spring loaded plunger that kicks the spent brass free of the action. It sounds as though the spring under your plunger is broken or gummed up, or perhaps the bolt face has a burr which prevents the plunger from moving freely.
There should be a cross pin that hold the plunger in place, this can be driven out, being careful not to loose the plunger that is under spring pressure. The recess can then be cleaned out, the spring examined for damage, and the mouth of the plunger's recess can be examined for any burrs. If the spring is broken, order another. In the meantime, you can continue to use the rifle without the ejector, but you will have to manually remove each fired case from the bolt face. If the recess is gummed up, clean it out with solvent, aerosols are good in this application, and Break-Clean will probably remove the offending material without manual scrubbing. Once the recess is clean, lightly lube the spring and plunger and reassemble. If you apply too much lube or too heavy a lube, the ejector won't work properly in the cold. If the mouth of the ejector's recess is burred, carefully chamfer the burr away with an appropriate hone or a Dremel, but it requires a light touch. After the burr has been removed, clean out the recess again, check the extractor to ensure it moves freely in the recess, lube it lightly and reassemble.
