Reporting live from Ecuador (terrible picture)

This is Jonathan Evans reporting from Ecuador, morning for all of viewers good morning to all the viewers. I am in at the epicentre of the earthquake, in the province of Manabí. Well, the situation here is a completely disaster, the main facilities are totally collapsed and hundreds of people wander about the streets with no water and foods.  (two options here: "...wander about the streets without access to water or food" or "... wander about the streets with no food or water.")

Yesterday, at 18:58 was produced, a terrible earthquake [ happened / occurred ] with [ a ] 7.8 magnitude. Buildings were shivering for three whole minutes. Many people died there have died, [ but ] it is still too soon for to knowing how many, and. Many others are in the hospitals.

At night, we are coming back with more news. More news tonight at [ time ].

It was Jonathan Evans.

Reasons:

morning to all viewers -> good morning to all the viewers.

    "good morning" is the full greeting. The full version is generally used in news programs due to it being slightly more formal.

in the epicentre -> at the epicentre

    Since the epicentre of an earthquake is a "point" location (i.e. a single place), and the earthquake is an event that you can't be literally "inside" of, we tend to use "at".

with no water and foods. -> either of the options

    Strictly speaking, a negative expression of similarity (i.e. no water /and/ no food) is formally written as:

               no water nor food.

    However, nor is not used often in spoken English, so you would use "or". News reporters use the phrase "without access to..." when describing the inability to get something.

at 18:58 was produced -> at 18:58,

    Grammar. The object is said before the verb in English, so the verb [ produced ] would be shifted to after the word "earthquake". Besides that, the choice of word is wrong. [ produced ] usually means it was something created by a human. We use the words [ occurred / happened ] for natural events such as earthquakes, floods, tsunamis.

Buildings were shivering for three whole minutes -> ???

    Your sentence is correct, but the verb here isn't quite as strong as it should be. For a powerful earthquake (7.8), you would want to use a more "violent" term. Shivering usually means very small, repeated movements. Example: Buildings were violently shaking for three whole minutes.

At night, we are coming back with more news. -> More news tonight at [ time ].

    Again, the sentence is correct. However, in the context, you are using a "passive" way of stating a future event. For a news program, or any formal speech, or anything that requires confidence, you should say it in a way that expresses it very concrete. Hard to explain, but essentially the modified version makes it a "promise" whereas your version makes it just an "event".

 It was Jonathan Evans -> Jonathan Evans.

    "It" is used often to refer to objects. We use he/she/they for referring to people. In this case, since you are referring to yourself, there is no need to state "it was" or "he was" since it is inferred from the statement "Jonathan Evans" without any other words.

Let me know if you're having trouble understanding things.

It's a pronunciation of the word "thing". In terms of music or slang, it usually refers to something sexual. "She's got a big thang" = She has a big ass. "He's got a big thang" = He has a big dick. etc.