M'ath!
Good job translating as a beginner, but there's one key component you forgot to use in you statement; the imperative mood.
The imperative mood indicates that you are commanding someone to do something, and looking at the phrase you want to translate it definitely fits under this definition. You can write the imperative in either the formal or the informal ways. Since this phrase is adressing an unknown audience, and since I assume you want this statement to have authority over the readers, I suggest using the formal imperative.
The formal imperative is rather simple to write. All you have to do is add /-i/ to the end of the bare verb form that ends in a constonant, and just the bare verb form with verbs that end in a vowel. Also, you leave the pronoun out of the phrase since this is imperative.
remember not to use the word nakhaan. First, it's an unessecary detail. Second, it doesn't agree with the case assignment laid out by the preposition hatif.
remember to use the conjunction ma!
And regarding your question of the Dothraki word for 'worship', I suggest using the word Joro (idol, icon) and turn it into a verb; Jorat (to idolize).
So, the final translation of, "Eat, Sleep, Drink, worship, surrender to game of thrones" should be;
"Adakhi, remeki, inde(), jori, ma allo() hatif Vilajerosh Adorisi"
imperative suffix is marked in red
conjunction is marked in purple
preposition and cooresponding declension is marked in green
