Hey there. Glad it is of some help until the official support rolls in.
The time taken for sync to reflect on other devices depends on Firefox sync itself. It is an eventual sync model. Which means, it sometimes takes longer for the sync to reflect.

I chose to use Firefox's sync feature for the storage instead of own private cloud based solution for few reasons:
* Safer for users to trust firefox than a random me
* Works until firefox stops supporting sync - long life guarantee
* I did not want to charge users for this plugin - using my own cloud would mean I will need to pay for the storage etc.. and will need to charge something from users.

Using a private cloud could have allowed me to provide instantaneous sync but the cons of that (primarily privacy/safety concerns) made me choose this path.

Bug 1: Can you share your OS and firefox version please? I would like to see if I reproduce this issue. Have not heard of this behavior yet - doesnt mean it cannot happen though, there is always a first time!. One known behavior - eg: if you have a logged in gmail under a tabgroup, opening it on a different device would automatically redirect the page to login. Which means, the tab(url) no longer matches the tab(url) on the initial device. So if you perform a sync again, its going to detect the missing url tab and will create one!

Bug 2: This is because of the firefox sync latency that I mentioned above. But the name should have reflected in both of your devices if it started working on one of your device.