Ma hétfő van. Peter az irodában van. Reggel kilenc óra van. Peter nagyon fáradt. Itt nincsenek bútorok! Hol vannak a bútorok? *

Egy egér van az ablak alatt.  ** Mi ez?! Siess! A másik épületbe, a harmadik emeletre, az ötös szobába! ***

Itt nincsenek bútorok a szobában. Csak egy virág.**** Ott a kulcs a virág mellett. 

Comments:
* in this case, the verb "lenni" ( = to be) has to be in its plural form 
** it sounds more natural to put the verb at the beginning or in the middle of the sentence. (Van egy egér az ablak alatt. / Egy egér van az ablak alatt.) The word order depends on the content you want to emphasize in your sentence. Don't worry, you definitely need time to feel how it works. :)
*** "Sietsz" means "you hurry" and "siess" means "[you] hurry up!" (imperative) and the suffixes indicate where to go 
**** It makes more sense to write "egy virág" (a flower), than "a virág" (the flower)

Very good start, keep it up! :)

My Hungarian Cartoon Story - Part 1

Hey there! First of all, I could grasp the meaning of your cartoon, but somehow the story in general seems incoherent for me. It was my first impression while reading the text as a native Hungarian speaker. I cannot explain this in more detail because I have nothing in common with teaching.  Anyway, most of your sentences are fine, but I found some minor mistakes. 

Let me give you some examples. 

- Hol van a bútorok? --> CORRECT: Hol VANNAK a bútorok? ( You did not set the "van" verb for plural form)  

- Sometimes, you haven't used the necessary accentuate letter with specific words. Examples: irodaban - irodÁban; faradt - fÁradt;  virag - viráÁ; regi - rÉgi.

In my opinion, these are ony tiny mistakes, however I found a sentence with no logical meaning.

- A másik épület a harmadik emeleten, az ötös szoba. I will try to translate this from Hungarian to English for you. It sounds like " The another building is the third floor, door number five.) 

Despite your first attempt of writing something complex in Hungarian, you did very well! It is quite surprising. Hungarian is not an easy language to learn. Hopefully,  I could help you with this short review. :)