Electronic – I2C Slave on ATtiny841

Toby says you'll need two I2C buses, but that's not necessarily so. In this answer I point at the information in the LPC930 datasheet how to switch between the two modes on the same bus.

I guess by "at the same time" you mean in one and the same application, and that's not so hard. If you want to write or read on the bus as master you wait until the bus is free, switch to master mode and start clocking. After the message is sent/received switch back to slave mode and listen for messages from other masters.

Electrically collisions are not a problem, since the bus is a wired-OR. Protocol-wise you may have a problem when two masters would claim the bus simultaneously, but then the message will be so messed up that you won't get an acknowledge, so you know you have to send it again. Most protocols will retry after a random time, which should be different for each master, so that the collisions don't keep repeating.

Alternatively, you can make a token-passing protocol of it, where the controller which has the token is master, and after doing its business, can pass the token to the other master. It then switches to slave mode, and waits until it receives the token back. Only then it can switch to master mode again.

The I2C module provides a way to identify erros, once you send, let's say a START condition or whatever you have to verify the TWSR register (TWI Status register) and it should match the state you are expecting (e.g. Aknowledge from slave). There is a flow diagram for each working mode showcasing the different status values.