Learn Farsi: شما نمی‌توانید بدون آب و غذا زنده بمانید. - You cannot stay alive without water and food.

Yes, the preposition bedun (without) needs an Ezafe to link it to the noun that follows it. You pronounce it bedun-e. Even though the word without applies to both water and food, the Ezafe only attaches directly to the preposition, giving us bedun-e āb o ghazā.

Why is the verb for stay written as bemānid?

It is in the subjunctive form because of the modal verb nemi-tavānid (you cannot). In Farsi, when you use verbs expressing ability, desire, or necessity, the action that follows must take the subjunctive prefix be-. That is why the verb māndan (to stay) becomes bemānid.

How does the compound verb zende māndan (to stay alive) handle this be- prefix?

For compound verbs, only the true verb part changes to match the grammar rules. The adjective zende (alive) stays exactly as it is, and the be- prefix is added only to the verb portion, resulting in zende bemānid.

How should I pronounce the و connecting water and food?

When connecting words in a pair like this, the conjunction و (and) is usually pronounced as a short o sound. You will hear native speakers say āb o ghazā rather than using the formal va pronunciation.