Learn Hardcore Russian: У меня есть привычка читать газету утром. - I have a habit of reading the newspaper in the morning.

In Russian, possession is normally expressed with the construction у + genitive plus (optionally) the verb есть. Literally У меня есть книга means “At me is a book.” The verb иметь (“to have”) exists but is rarely used in everyday Russian for simple possession.

Can we omit есть in this sentence? If so, does the meaning change?

Yes. In present tense you can drop есть and still say У меня привычка читать газету утром. The meaning remains the same. Including есть simply adds a bit more emphasis on the fact that the habit exists.

What case is меня, and why must we use it?

Меня is the genitive form of я. After the preposition у, the possessor always takes the genitive case: у + genitive.

What role does привычка play, and why is it in the nominative case?

Привычка (“habit”) is the noun you “have.” As the subject of the possession construction, it stands in the nominative case.

Why is читать used in the infinitive form here instead of a conjugated verb?