Learn Finnish: Vanha tehdas purettaisiin. - The old factory would be demolished.

You build it from the basic present passive. The present passive of purkaa is puretaan (is demolished). To make it conditional ("would be"), you drop the final -an, double the t, and add the passive conditional ending -isiin. This gives you purettaisiin.

Why does the a from purkaa change to an e in purettaisiin?

This is a standard rule for Type 1 verbs ending in -aa or -ää. When you put them into the passive voice, that final a or ä changes to an e. You will see this same vowel change in words like antaa (to give) becoming annettaisiin (would be given).

Why doesn't the object vanha tehdas end in -n (like vanhan tehtaan)?

In active sentences, a whole object usually takes the -n ending (the accusative/genitive case). However, in passive sentences, a whole object is always put in the basic nominative (dictionary) case. Because purettaisiin is a passive verb, vanha tehdas drops the -n.

Could this sentence also mean "We would demolish the old factory"?