Translation:In my city, there is a Christian church and a Muslim mosque.
In Greek it's more common to use singular form of the verb υπάρχει if the following noun is singular. It's not wrong to say υπάρχουν, though. So, στο καλάθι υπάρχει ένα μήλο και (υπάρχει, omitted) ένα πορτοκάλι. Or (less commonly used) στο καλάθι υπάρχουν ένα μήλο και ένα αχλάδι (where you consider the "ένα μήλο και ένα αχλάδι" as the following noun, and there is no omission implied). It's also correct with other verbs. Στην αυλή παίζει ο Γιάννης και ο Κώστας=In the yard, Giannis and Kostas play. But that is never the case when the nouns preceede the verb. So Ο Γιάννης και ο Κώστας παίζει στην αυλή is completely wrong, must be παίζουν. Hope that clarifies it a bit.
You are wrong. In English, it is not correct to use "there are" in this sentence. This is because you are talking about two single buildings separately. You would only use "there are" if you were referring to more than one of the same type of building. For example, "there are two churches and two mosques".
I've been looking into this (and I've learned some things about English in the process). I think "not correct" is too strong. The general consensus is as you say, but it appears to be guidance rather than a rule, and there is not 100% agreement. See near the bottom of this page: https://www.grammarly.com/blog/there-is-there-are/
A temple, at least for me, is often bigger or more important.
Most Christian denominations don't use the word "temple" for their own buildings at all.
Solomon built a temple in ancient Israel - a special building.
"Temple" is often used for pagan (non-Abrahamic) buildings, e.g. "temple of Poseidon" or "Hindu temple".
Latter-day Saints ("Mormons") have temples which are distinct from churches - their temples are for specific sacred ceremonies rather than weekly worship ceremonies.
I see... In Greek ναός is used for any religious building whereas εκκλησία is used for Christian churches only (or mostly). Εκκλησία also has the meaning of the "religious gathering". You will never say Η εκκλησία του Ποσειδώνα but you will have to say Ο ναός του Ποσειδώνα. So ναός in Greek is wider than temple in English, I think...
But when speaking English, Orthodox Christians, even non-Greeks usually refer to the Church building as the Temple, and the community as the Church, although you do hear that Temple and Church used interchangeably for the building, mostly in the West due to Western influence. Context tells you whether Church refers to the building, the community, or both.
If you look at the comments below, you will see that ναός can be used in Greek for christian churches, but "temple" is avoided to be used in English for Christian churches. Anyway, there is an accepted translation with "temple". Consider that in Greek, when talking about christian churches, the words "ναός" & "εκκλησία" are synonyms.
As a Greek Orthodox Christian in an English speaking country, I can assure you that we do call the Church building the Temple. I have heard the same at a Ukrainian Greek Catholic Church. As a former Roman Catholic and former Greek Catholic, my experience has been that this is exclusive to Eastern Christianity. Western Christian Churches woukd call the building the Church or the Sanctuary.