I'm a native English speaker and using no article in this sentence doesn't sound natural.
"This egg is for the salad." The salad you know that I'm making for dinner. Or...
"This egg is for a salad." I'm saving it for a random salad I will be making in the next couple of days.
"This egg is for salad." Does not sound natural at all, nor is it clear if the person you are speaking to is aware of the salad or not.
That would be "Это — яйцо для салата". The em-dash replaces the verb "to be", which would've been placed just like in English in both cases if it wasn't omitted. Granted the dash is mostly optional, so without it the sentence could've had both meanings. But since it's here, it's placement is important. In fact its main purpose in such cases is specifically to clear up potential confusions like this one.
Prepositions come with case requirements of their own. Для is one of many prepositions that only ever use the Genitive.
A few prepositions have a larger list of meanings, and some groups of these meanings require different cases.
- For example, c paired with the Genitive generally means "down from, off" whereas used with the Instrumental it means "(together) with".
It will not be correct. English "for" has multiple uses, and those of за and для rarely intersect.
- для is used as "for the benefit of", "with the purpose of"
- за is "for" as the opposite of "against"
- за is "for" in "I bought it for $20". It means getting or doing something in exchange for something
- за is used to express how long it takes to perform some action. English "for" is not used in this meaning.
- "for" is used to express how much time you spent doing something (which does not mean you are finished, and are no longer going to do that). Russian does not use any prepositions for that, and just uses Accusative.
- за also has the literal meaning of "behind". It is used with Instrumental (for position) and with Accusative (for direction).