Learn Icelandic: Má ég reykja hérna?

Because it follows the modal verb mega (to be allowed to). Just like in English (where we say 'may I smoke' instead of 'may I to smoke'), Icelandic modal verbs take a bare infinitive. This means you use the dictionary form of the verb but leave out the word að.

Má looks very different from its dictionary form. What is the infinitive?

The infinitive is mega. Modal verbs in Icelandic often have irregular conjugations. Má is the correct present tense form for both ég (I) and hann/hún/það (he/she/it).

What is the difference between hérna and hér?

Both words mean 'here' and they are practically interchangeable in everyday conversation. Hérna is extremely common in spoken Icelandic and is often used when pointing out a specific spot, while hér is slightly more neutral or formal.

Why does the sentence start with the verb má?

Because it is a yes/no question. Just like in English, Icelandic creates these questions by moving the main verb to the very front of the sentence, placing it before the subject ég.