articles - time expression + has/have

After ten years has passed you can apply for possession of the land.

Ten years have passed - ten long, lonely years - since Bill died at sea.

I wonder why is there has in first sentence?. I know if we use it as "a period of ten years" then we can use has.

"A short ten years has brought us to this point."

"An arduous ten years have passed."

Here in #2 it(Ten year's) modified by article that makes it countable. So there should be Has in both sentences of example #2. Correct me if i am wrong.

Answer

After ten years has passed you can apply for possession of the land.

Well, you basically answered this yourself. But I would express the usage as 'ten years' is considered singular.

As you noted, we use this in time phrases. We also use this in money phrases, such as 'Ten dollars is all I have.'

A short ten years has brought us to this point.

Here the same thing is happening. Ten years is considered singular, so both a singular verb and the indefinite article is used. (The indefinite article may only be used before count nouns, and count nouns are singular; that is, non-count nouns cannot be plural.)

I can also say

A ten years has passed that I will never forget.

Again, ten years is considered singular and so I can use a singular verb, and I can use the indefinite article before the singular 'ten years'.

The question seems to be about the following:

An arduous ten years have passed.

We know that with "arduous" we can say:

An arduous ten years has passed.

Ten years is considered singular, and the indefinite article may be used before a singular noun. In addition, an adjective may modify a singular noun.

So the question remains, can we say

An arduous ten years have passed.

Here, 'ten years' is considered plural, a plural form of the verb has been used, an adjective has been used, BUT an has been used. We know an goes only before singular nouns. So there does seem to be a conflict.

Despite this, the usage seems fine to me. There are other expressions in which we use the indefinite article an with in an expression that uses a plural verb form:

A good many days have passed.

A few days have passed.

A number of people are marching down the street.

A large number of complaints have been received.

A lot of horses recently have been coming around the mountain.

A hundred people have gone home after waiting an arduous ten years.

Pethaps it is possible that the idea of ten years being considered singular OR plural is similar to a collective noun (example: team, crowd, government) being considered singular or plural:

The team is unbeaten after playing ten games. (US)

The team are unbeaten after playing ten games. (UK)

Thus, maybe the following is possible:

? A lucky England football team have won the world cup.

I don't know if the above would actually be said (maybe the idea is too preposterous to consider). But the following has been said:

An eager team have knitted and crocheted 120 squares including 4 complete blankets.