Learn Farsi: این هتل اصلاً اینترنت ندارد.

That symbol is called a tanvin, which Farsi borrowed from Arabic. It tells you to pronounce the end of the word as "-an", so this word is pronounced aslan. In written Farsi, this "-an" ending is used to turn certain Arabic loanwords into adverbs.

Why does اصلاً (aslan) translate to "absolutely no" instead of just "absolutely"?

The word aslan translates more literally to "at all" or "absolutely." The negative meaning in the English translation actually comes from the negative verb at the end of the sentence: nadârad (does not have). It is extremely common in Farsi to pair aslan with a negative verb to mean "not at all" or "absolutely no."

Why doesn't اینترنت (internet) have the direct object marker را (râ) after it?

The marker râ is used only for specific direct objects (like "the specific internet we talked about"). Because the hotel is missing internet in a general, indefinite sense ("any internet"), you don't use râ.

How is the verb ندارد (nadârad) formed here?

It is the negative present tense form of dâshtan (to have). The present stem is dâr, and for "it" (the hotel), we add the ending -ad to get dârad (it has). To make it negative, we add the prefix na- to the beginning, creating nadârad (it does not have).