If I was to start paying the subscription fee for Vendetta, would I be able to play the game on PC and on android? Not necessarily using the same characters, but would I have access to the game on both?

Yes, and yes you will have access to the same characters/account

Your characters and inventory are all stored on the server, but stuff like your mission log and sector notes are stored locally by the game client. You can log in and play with the same account from any of your devices, but don't freak out if your notes are missing.

But you cannot play on both devices at the same time. Logging in with one device will log you out of another.

Is it correct behaviour that Mission Logs are not shared between PC and Android versions? So you can't see which missions you have finished on other device?

Yeah mission logs are stored locally on the device.

The licenses and accomplishments for unlocking things are stored server-side with your character though, so its not like you lose access to anything except for the archived mission text.