Hi Nate385,
Nice question, thank you!
The Passive voice in Russian is mainly used in written speech. There are 3 types of the passive voice: the Present, the Past and the Future.
The Present tense form of the Passive voice can be built in 2 possible ways:
1. By adding the particle "ся" (process; repetitive action):
Школа строится: The school is being built.
Работа пишется студентом: The work is being written by the student.
2. By using the short form of the Present passive participle (result, fact):
Его оперы любимы публикой.
His operas are loved by the public.
The agent (smth is done by smb) is always used in the Instrumental case. It works for all the types of the Passive voice.
The Past tense of the passive voice is formed by the verbs был, была, было, были and a short form of the past passive participle, depending on the gender of the subject.
В Москве в прошлом году были открыты шесть новых кафе "Шоколадница": 6 new "Shokoladnitsa" cafes were opened in Moscow last year.
Петербург был основан Петром Великим: Saint Petersburg was founded by Peter the Great.
If the result of an action is preserved in the Present and if the attention of the speaker is focused on the situation rather than on the action itself, the verb "быть" can be omitted.
Работа сделана: The work is done.
The Future tense of the Passive voice if formed by the verbs буду, будешь, будет, будем, будете, будут and a short form of the passie past participle.
Товар будет закуплен и отправлен: The goods will be bought and sent.
Газеты будут проданы: The newspapers will be sold.
As for your examples, the correct version is:
Он мне разрешает: Мне разрешено (Мне разрешается)
Я строю дом: Дом строится мной
Он говорит мне: Мне сказано (Мне говорится)
Best,
Yulia Amlinskaya,
Russian language teacher.