1. It depends. "work" can be both countable and uncountable. 

For example:

Teaching is excellent work (uncountable)

That painting is an excellent work (countable)

So when the noun takes an uncountable noun it is incorrect to add the article. 

For example:

This is delicous rice. 

South Africa produces interesting music.

The house is covered in grey dust.

Make

Form: make + person + verb

Use: to force someone to do something

Examples:

My teacher made me apologize for what I had said.
Did somebody make you wear that ugly hat?
She made her children do their homework.

Have

Form: have + person + verb

Use: to give someone the responsibility to do something

Examples:

Dr. Smith had his nurse take the patient's temperature.
Please have your secretary fax me the information.
I had the mechanic check the brakes.

Get

Form: get + person + to + verb

Use: to convince to do something" or "to trick someone into doing something.

Examples:

Susie got her son to take the medicine even though it tasted terrible.
How can parents get their children to read more?
The government TV commercials are trying to get people to stop smoking

Dear,Jessie how we makes these types of sentences

he has a letter written.

he gets a letter written.

he makes me write a letter.

i am made to write a letter.

 please explain each example in comprehensive way and give more examples.

if we use an uncountable noun after adjective then adjective will article or not .

means adjective+uncountable noun

1. Yes.

"A" before adjectives starting with a consonant sound.

"An" before adjectives starting with a vowel sound.

Most any noun would work, countable or uncountable.

"An excellent work" is correct grammar. However, how natural it sounds depends on what you mean by "work" (context). If you mean "work" as in 'a work of art, literature, etc' this sounds pretty good (natural, although there may be better or more acurate words to use to describe it). If you mean "work" as in "I'm at work" then this wouldn't be right. You would say "job" as in 'an excellent job'. Then, job could mean two things, a job as in 'a place to work' (ex. He has an excellent job as a lawyer for J Law Firm) or 'something that you do' (ex. Good job! You did an excellent job!).

More examples ...

A delicious apple

A hairy spider

A tall tree

An orange room

An obnoxious voice

An evil woman

The big horse

The modern room

The sad eyes