differenceword-choice
import {noun}:
1. (usually imports) A commodity, article, or service brought in from abroad for sale:
2. [in singular] The implicit meaning or significance of something
How do 'importance' and definition 2 of 'import' differ? I ask not about definition 1 above that 'importance' lacks.
As I commented, I don't have an answer for your question #2. But I can help you with your question #1. The resources you were trying to access and can't seems to redirect to Fowler's Modern English Usage page. Even I don't have access to that page, but I have an image of that page from that book. Here is that page. Please have a look -
Download this image from here
I basically agree with SoltBegins, but let me state it a different way.
To "give effect to" something is to make it work, to make it carry out its desired intent.
To "effect" something (as a verb) is to bring it into existence or make it happen.
So if you said, "Mr Smith effected an agreement between the parties", that would mean that Smith managed to convince the parties to come to some compromise. Like, he convinced them that they should each pay half the cost. If you said, "Mr Smith gave effect to the agreement between the parties", that would mean that he did something to make the agreement actually happen, like he collected the money from each of them.
Addendum
To try to answer your question:
By "make it happen" here I mean something along the lines of "bring it into existence". Maybe it would have been more clear if I'd just left it at "bring it into existence".
"Give effect to" specifically means to cause something that previously existed only as an idea or on paper to actually happen. We routinely talk about "giving effect to a contract" or "giving effect to the new law".
To "effect" simply means to cause, or cause to exist. Sometimes, often, causing something to exist and making it happen are the same thing. When we say "Smith effected X" we often mean that he both caused it to exist and caused it to produce the desired outcome. If, for example, you say "I effected an update to the document", making the update exist and making it actually change the document are probably a single event, you can't separate them out. So in a given case,
whether "to effect X" means to create a concept that is not yet actually happening in the real world,
or if it means both to create the concept and to really make it happen, depends on the context.
In the case of an agreement, if all the parties are truly willing it might be that once the agreement is made, they all go off and do whatever, and no one thinks of a separate step of giving effect to the agreement. It just depends on context.
Best Answer
Import is rarely used to mean "significance" outside of formal/academic writing. Importance is used for this purpose in nearly all cases.
This isn't simply a difference between casual conversation and formal writing. I'm a reasonably well spoken and well read native speaker of American English who is not afraid of using my vocabulary, and I would be surprised if I had ever used that meaning in conversation before. Importance is far more common, probably even in formal and academic writing. In modern writing, import seems to be used as a way of making writing sound more sophisticated or in fiction, to make a character seem pompous.