Learn Arabic (Modern Standard): كان هذا المسجد مبنى تاريخيا.

Because of كان (was). When you use كان, the describing part of the sentence (the predicate) must be in the accusative case. For indefinite words, this usually means adding an "-an" sound (double fatha) and an extra alif, turning تاريخي into تاريخيا.

If "building" (مبنى) is also part of that describing phrase, why doesn't it get an extra alif too?

The word مبنى ends in an alif maqṣūra (ى), which looks like a dotless yaa but sounds like an "a". Words ending in this special letter never change their spelling to show case endings. Even though it is grammatically in the accusative case here, it stays spelled exactly as مبنى.

Why does "mosque" have the definite article الـ (the) attached to it, making it المسجد?

In Arabic, to say "this [noun]", the noun must be definite. So, هذا المسجد is how you say "this mosque" (literally: "this the-mosque"). If you left off the الـ, you would get هذا مسجد, which means "This is a mosque"—a complete sentence on its own!

Why does the verb كان come before the subject "this mosque"?

This is the standard word order in Arabic. Arabic usually puts the verb before the subject (Verb-Subject-Object). So, the sentence literally reads: "Was this the-mosque a building historical."