Q: What could happen by driving without a bolt on a pulley?

The consequences in regard to the pulley depend on which pulley was vandalized (there are quite a few on a engine). If it was the crank pulley, such could fall off (eventually) and if it does cause a fair amount of damage if it happens while the engine is running. Indeed, if it’s the crank pulley and the harmonic balancer comes off with it and the engine continues to run that can damage the crankshaft. That would be very bad. Other pulleys could get distorted if a fastener is missing and in such condition could damage the drive belt riding on the pulley. Putting engine oil in the transmission is not a good idea and the transmission will have to be thoroughly drained. If you know there is engine oil in the transmission try not to to start the car because that will further contaminate the transmission and make it more difficult to get the oil out. If you have not driven it, which again is the best scenario, simply remove the transmission oil pan and let all fluid everything drip out thoroughly. You might have to go through a couple drain/refill cycles. YourMechanic does offer a transmission fluid exchange service which you can request.