"Niirisallapreĝejosamtempe."

-ej- means a place where you do something, just like kafo - kafejo

Dankon

According to Wiktionary, you're correct. Source: https://en.wiktionary.org/wiki/pre%C4%9Dejo.

I reported it.

Temple is an accepted alternative.

Yeah but the creators of the English to Esperanto course seem to like pushing Christianity into the course. It's kind of annoying

Technically it means any place where people gather to pray, and you can certainly use it for other religious buildings. But it's commonly understood to refer to a Christian church, and that's given as its secondary definition in PIV.

There are other words for religious buildings in Eo, such as: baziliko (basilica), kapelo (chapel), katedralo (cathedral), kirko (church), moskeo (mosque), pagodo (Buddhist or Hindu temple), sinagogo (synagogue) and templo (temple).

Whether you use these or use preĝejo is going to be down to context - if you're in a group of Japanese Shintoists, preĝejo may be taken differently from how it's used by a group of Eo speakers from a Christian majority country.

Simultaneously. Source: https://en.wiktionary.org/wiki/samtempe

"Pregxejo" is a generic term for a place of worship. Mosque is "moskeo", church is "kirko", synagogue is "sinagogo" and temple is "templo".

I would think so, since a mosque is also considered a place of prayer. I recommend, if it isn't then report it. There is a specific word for mosque - moskeo, but I think preĝejo can be mosque, according to context.

Mi pensas vi ŝerĉas la vortojn de "sama tempo". Ĉu vi ne? La vorto de "samtempe" estas adverbo, tiel ni povas diri "simultaneously" anstataŭ "at the same time".

Mi pensas ke ne fartu.

I believe it's because al already assumes movement, so it'd be redundant.