Someone can correct me if I'm wrong but this is how I understand it.
Near and Nearly
Source: Grammarly Handbook
Nearly is an adverb, which means almost; near is a flexible little word which can be an adjective, verb, adverb or preposition.
This means that both of the following are correct:
This essay is nearly complete.
This essay is near-complete.
If we switch to "Nearly universally", we are now dealing with "near" + adjective + noun.
An example sentence could be:
This essay is nearly universally accepted.
This essay is near-universally accepted.
Here, some minor ambiguity is possible because there are two modifiers and a noun. To me, these both can have different meanings, if only slightly.
This essay is nearly universally accepted. The essay is very close to being "universally accepted".
This essay is near-universally accepted. The essay is accepted "almost universally".
Nearly modifies accepted while Near- modifies universal.
Usage
Neither of them sound great to me and neither is widely used. But of the two, nearly universally is more common according to Google NGrams.
I recommend skipping both and rephrasing into something cleaner.
Native speakers say to the best of my knowledge when speaking a bit formally.
They almost never say as far as my knowledge goes, which is understandable but alien.
As far as I know is fine and less formal than to (the best of) my knowledge.
Best Answer
Authentication (in this sense) is the confirmation that the person who is giving a command or placing an order is the person they say they are. In other words, they are making sure that this person is authentic or can be identified.
Authorization means that you are giving permission to do something. So, if you authorize something, you are saying I allow this based upon my authority.
They are related, but different.
For example: An app can ask for your authorization to make a purchase, then it will attempt authentication in the form of a password.
To answer your second question: Authorisation is an accepted secondary spelling of authorization. But, in American English, authorization is the preferred spelling.