Translation:The dog is going to be in the garden.
I believe estarse is the verb for 'to stay'. Here is a link
"Estarse" is just another form of the verb "estar". Sometimes a sentence that has the verb "estar" in it can be translated to English as "to stay" and keep its meaning, because some times they could share the scenery in which they can be used, but again "estar" is not to stay. For example "Él va a estar en mi casa hasta enero." Can be translated as "He is going to stay in my house until January." Or "He is going to be in my house until January. " The verb for "to stay" is "quedarse", "Él va a quedarse en mi casa hasta enero." = "He will stay in my house until January."
That's not really how ser and estar work.
You could use more specific verbs like to be buried in the garden, but the idea would still be estar en el jardín.
That's the downside of simplifying them into temporary vs permanent. That logic breaks down when you think of things like "soy joven" or "estoy muerto"
Ir has 6 conjugations, just like all other verbs: yo voy, tú vas, él/ella/usted va, nosotros vamos, vosotros vais (a subject not learned in this duolingo Spanish), and ellos/Ustedes van. So, when I use the phase "someone is going to do something" I use the structure Ir+a+infinitive, meaning that I choose the subject and conjugate ir to fit, put "a", and then leave the infinitive (unconjugated) verb. For example, if I wanted to say "We are going to cook dinner" I would say "Vamos a cocinar la cena." If I left the first verb ir unconjugated, the sentence would not have the correct subject and the meaning would be lost.
I think the difference is because of the verb "estar." There is a difference between the dog going to the garden (shows movement) and that the dog will be in the garden (doesn't indicate movement). This phrase is helpful for "if you need me, I'm going to be in thr garden" and other examples