The Greek source of "for" is a word that means "that" or "because." 

The word translated as "there" is the Greek word commonly translated as third-person pronouns in English.   This "they" follows the phrase about days. It seems to refer to the "days".

The verb "be" here is the common form of "to be" in Greek. It means to have a certain characteristic or remain in a certain condition. It also equates terms or assigns characteristics. This verb ends the clause.

There is no "the" here.

The Greek word translated as "days" also means "time," in general, and refers specifically to the "daytime."  This phrase starts the verse so it is important.

"Of vengeance," is a noun that means both "vengeance" and "satisfaction". The sense is that people are satisfied with vengeance.  Luke only uses this term  once earlier, with an article.

The word translated as "that" is the Greek definite article, which usually precedes a noun and, without a noun, takes the meaning of "the one."  This article actually precedes the verb translated as "may be fulfilled", which is not active and appears after this word, not at the end of the clause.  The Greek article is much closer to our demonstrative pronouns ("this", "that", "these", "those"). See this article for more.  The form is genitive so it acts like our preposition "of" or "part of". See the verb at the end of the sentence for more about how this word works in the clause.

The word translated as "all things" is the Greek adjective meaning "all", "the whole", "every," and similar ideas. It is not used as a noun here, but an adjective affecting "which has been written". The "things" make it look as though it acts as a noun, which it really doesn't here.

The word translated as "which" is the Greek definite article, which usually precedes a noun and, without a noun, takes the meaning of "the one." The Greek article is much closer to our demonstrative pronouns ("this", "that", "these", "those"). See this article for more. 

"Are written" is the Greek verb that  means "to mark", "to express by written characters", "to write a letter", "to write down [a law]", and so on. The form is an adjective, but with the preceding article it acts like a noun, "that which has been written". It is in the same form as "all".

"May  be fulfilled" is a verb that means "to fill", "to fulfill," and "to fill full." The form, however, is not that of an active verb or an adjective. It is an infinitive that, when preceded by an article, as it is here, acts like a verb describing the action.  The form is passive, that which is being fulfilled. We would use the word "fulfillment". The form is genitive because of the article preceding it. It describes "days", not "what was written, which comes afterward.