When there is no article, you can usually add an indefinite article and it means the same thing. Not the other way around though.
The difference in cases like this between adding an indefinite article ("o") and not adding one is very small.
Kind of like saying: I have no spoon = Nu am lingurita I don't have a spoon = Nu am o lingurita
Should probably learn it as it is, I don't see it making much sense as a native speaker anyway
Not entirely sure, but no Romanian (in my experience) would use the indefinite article here. Actually, they tend to drop it more often than not. I speak with a lot of Romanians and this is normal. However, the difference that they are making between teaspoon and spoon is inconsequential in the actual use of the language.