I have a question about the word υπάρχει. I thought it implied more than "there is." Technically, isn't it best translated "there exists?"
Can be "there is" or "exists". So: Υπάρχει φαγητό στο ψυγείο=there is food in the fridge, Fairies do not exist=Δεν υπάρχουν νεράιδες.
So Υπάρχουμε, υπάρχετε and υπάρχούν would be there are?
Υπάρχουμε=we exist, υπάρχετε=you exist (plural), υπάρχουν=they exist/they are.
I put "it is a delicious watermelon" and it was marked wrong. I guess that would be αυτό είναι ένα καρπούζι or just Είναι ένα καρπούζι.
Yes, that's right.
There exists a delicious watermelon should be correct
It's marked wrong because we wouldn't say that in English for the same context.
So is Υπάρχει a short term version of είναι? i.e. Είμαι John but Υπάρχω 'some random emotion like hungry'? I will always be John but my hunger is a temporary thing? Kind of like soy and estoy in Spanish?
No, υπάρχει means exists, there is. Είναι is used for temporary and non temporary statements. There is no such distinction in greek as there is in Spanish. :)