Please, tell me about sync restrictions in free version of todoist. How often it is, how many devices and applications can i have?
There are no restrictions aside from one - you will need to sync your data manually (tap on the sync icon on the mobile apps). You can use Todoist on as many devices and platforms as you like.
I am on the verge of upgrading to premium to get notes and automatic syncing?
If I upgrade to premium does it automatically sync on all devices?
Yes, it syncs automatically if you're connected as you make changes, however in one particular case, you'd have to refresh the page manually, that is - when you make changes on mobile and are also logged into Todoist on the web and have it opened, then even though the mobile app will sync the changes, you'll have to refresh the page on the web to see the changes.
However, this will change soon as we will implement forced reload of the web-app so you won't have to refresh it either.