Finishing the Norwegian tree...
Will get me to what level? Will I be able to have fluent conversations in Norwegian after completing the tree?
I would say the only way to get fluent is through having conversations, and finishing the tree equips you to start having those conversations.
Also, it makes a huge difference whether you simply complete all the lessons and don't look back or repeat past lessons. A lot of the words you won't encounter the first time around, and even if you do, won't stick in your head if you don't repeat them.
That said, the tree covers just about all the grammar you need initially, a lot of vocabulary and some expressions. Everyday expressions is where I still feel most helpless after having completed the tree.
You should have some ability to converse and communicate but in my experience learning to have a fluent conversation is more about communication skills than things like perfect grammar. I believe it will help a lot but make sure you practice if you can and study elsewhere or you will just end up being really good at Duolingo.
I imagine you should be able to communicate just fine. But a slight complaint I often hear, is that people struggle (in varying degree) with the spoken dialects, since you never learn much about them.
Like any other language, practice makes perfect. And if you show willingness to learn, then there's no doubt you will succeed, eventually.