Can you use a food grade plastic container instead of a crock to make pickles? Or any other type of container?

Don't use plastic, you won't like the results nearly as much. I would suggest using gl. When I buy pickles from the store or buy jam, mayo, etc (anything in a gl container), I just save the container, clean it REALLY well and then set it aside until I'm ready to make some tasty home-made pickles. If you don't have anything like that, you can go to the store and decent sized jar for cheap.