[Casiopea]

1. *There have many reasons why Hong Kong people are considering job opportunities on the Mainland. <ungrammatical>

First of all, the word There isn't the problem. With expletive-there constructs, the structure is, there = subject. That is, the subject comes after the verb,

There are trees in the park. <subject>
Trees are in the park. <subject>

Note that, The structure There are trees is an incomplete expletive-there construct. Additional information is required; it can be implied (covert) or stated (overt); e.g., There are trees (over there).

In 1., the subject is 'many reasons',

There are many reason why Hong Kong people ... <subject>
Many reasons exist why Hong Kong people ... <subject>

Forms of the verb BE (am, is, are, was, etc.) are copular by function (X = Y ;i.e., There = subject), whereas the verb "have" is a transitive verb; it takes a grammatical object. Below, 'many reasons' functions as the grammatical object of "have", which is why 1. is ungrammatical.

1. *There have many reasons why Hong Kong people are considering job opportunities on the Mainland. <ungrammatical>

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2. *It is no doubt that shortage of clean water is a problem many countries will face in the future. <ungrammatical>

With expletive-it constructs, the subject comes after the verb: It = subject,

*It is no doubt that shortage of clean water is a problem many countries will face in the future. <subject>

*That shortage of clean water is a problem many countries will face in the future is no doubt. <subject>

As for the reason 2. is ungrammatical, here's hint,

There is no doubt in my mind (location) <grammatical>

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3. *By the time the fire was extinguished, there were five fire trucks arrived at the scene.

Firstly, were arrived is not a verb form in English. Secondly, the main clause has too many finite verbs. In English a simple sentence has only one finite verb,

There were fire trucks at the scene. <grammatical>
Fire trucks arrived at the scene. <grammatical>

With expletive constructs, there are two subjects, the structural subject (It or There) and the grammatical, or true subject (e.g., five fire trucks). In 2., the grammatical subject is linked to two finite verbs were and arrived, which is why 2. is ungrammatical.

there were (verb) five fire trucks (subject) arrived (verb)

Hope that helps.

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